subject:(Crank Nicolson)

Technical University of Lisbon

1. Marques, Catarina Neto. Option pricing under variable volatility.

Degree: 2017, Technical University of Lisbon

URL: https://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/14171

►

Mestrado em Mathematical Finance

A teoria de valorização de opções que conhecemos hoje em dia deu o seu maior passo quando Fischer Black e Myron… (more)

▼

Mestrado em Mathematical Finance

A teoria de valorização de opções que conhecemos hoje em dia deu o seu maior passo quando Fischer Black e Myron Scholes escreveram um artigo com uma fórmula fechada que permitia calcular os preços de opções Europeias de compra e venda cujo subjacente é uma acção ou um índice. No entanto, evidências mostram que a fórmula anterior não funciona bem num grande número de situações reais: os preços estimados desviam-se significativamente dos preços de mercado. Isto deve-se às hipóteses, muito restritivas, em que o modelo está assente. Esta dissertação alarga o modelo de Black-Scholes a situações em que a volatilidade do preço do ativo é variável. As implicações desta extensão são estudadas tanto de um ponto de vista teórico como prático. Existem muitos modelos propostos para o caso em estudo e este trabalho foca-se nos modelos de volatilidade local porque mantêm as características mais importantes do modelo original. Foram selecionadas quatro funções diferentes para descrever a volatilidade do preço do ativo e um método de diferenças finitas foi implementado para obter estimações e previsões do preço de opções. Os resultados obtidos realmente indicam que os modelos de volatilidade local estimam melhor os preços das opções do que o modelo de Black-Scholes original.

The modern theory of option pricing gave its biggest step when Fischer Black and Myron Scholes wrote a paper with a closed form solution for the prices of European call and put options on a single stock or index. However, evidence shows that the former formula no longer holds in many real cases: the estimated prices deviate significantly from the market ones. This is due to the very restrictive assumptions on which the model is based. This dissertation extends the Black-Scholes model by making the volatility of the asset price variable. The implications of this extension are studied from both theoretical and practical points of view. Several models have been proposed and this work focuses on the local volatility models because they maintain the most important features of the classical model. Four different functions were selected to describe the volatility of the asset price and a finite difference method was implemented in order to obtain the estimations and predictions of the option prices. The results suggest that indeed local volatility models have a better performance than the classical Black-Scholes model in estimating option prices.

info:eu-repo/semantics/publishedVersion

Advisors/Committee Members: Janela, João, Simões, Onofre.

Subjects/Keywords: Valorização de opções; Volatilidade local; Método de Crank-Nicolson; Calibração; Option Pricing; Local Volatility; Crank-Nicolson scheme; Calibration.

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Marques, C. N. (2017). Option pricing under variable volatility. (Thesis). Technical University of Lisbon. Retrieved from https://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/14171

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Marques, Catarina Neto. “Option pricing under variable volatility.” 2017. Thesis, Technical University of Lisbon. Accessed March 06, 2021. https://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/14171.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Marques, Catarina Neto. “Option pricing under variable volatility.” 2017. Web. 06 Mar 2021.

Vancouver:

Marques CN. Option pricing under variable volatility. [Internet] [Thesis]. Technical University of Lisbon; 2017. [cited 2021 Mar 06]. Available from: https://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/14171.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Marques CN. Option pricing under variable volatility. [Thesis]. Technical University of Lisbon; 2017. Available from: https://www.rcaap.pt/detail.jsp?id=oai:www.repository.utl.pt:10400.5/14171

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

2. Lopez, Victor Lopez. Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods.

Degree: Educational Sciences and Mathematics, 2016, Mälardalen University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32332

► Due to the interesting financial moment we are living, my motivations to write this Master thesis has mostly been the behavior of interest rates… (more)

Subjects/Keywords: Hull White; Swaptions; Negative interest rates; Crank-Nicolson

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lopez, V. L. (2016). Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods. (Thesis). Mälardalen University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32332

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lopez, Victor Lopez. “Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods.” 2016. Thesis, Mälardalen University. Accessed March 06, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32332.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lopez, Victor Lopez. “Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods.” 2016. Web. 06 Mar 2021.

Vancouver:

Lopez VL. Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods. [Internet] [Thesis]. Mälardalen University; 2016. [cited 2021 Mar 06]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32332.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lopez VL. Swaption pricing under the single Hull White model through the analytical formula and Finite Difference Methods. [Thesis]. Mälardalen University; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-32332

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Jonsson, Tobias. On the one dimensional Stefan problem : with some numerical analysis.

Degree: Mathematics and Mathematical Statistics, 2013, Umeå University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215

► In this thesis we present the Stefan problem with two boundary conditions, one constant and one time-dependent. This problem is a classic example of… (more)

Subjects/Keywords: Stefan problem; heat equation; crank-nicolson; finite differences

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Jonsson, T. (2013). On the one dimensional Stefan problem : with some numerical analysis. (Thesis). Umeå University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Jonsson, Tobias. “On the one dimensional Stefan problem : with some numerical analysis.” 2013. Thesis, Umeå University. Accessed March 06, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jonsson, Tobias. “On the one dimensional Stefan problem : with some numerical analysis.” 2013. Web. 06 Mar 2021.

Vancouver:

Jonsson T. On the one dimensional Stefan problem : with some numerical analysis. [Internet] [Thesis]. Umeå University; 2013. [cited 2021 Mar 06]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jonsson T. On the one dimensional Stefan problem : with some numerical analysis. [Thesis]. Umeå University; 2013. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-80215

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Minnesota

4. Dahlman, Erik. Mathematical models and simulation of tumor growth, radiation response, and micro-environment.

Degree: PhD, Biophysical Sciences and Medical Physics, 2019, University of Minnesota

URL: http://hdl.handle.net/11299/211744

► Reaction – diffusion based tumor models have been used to explore tumor growth for the past 30 years. These models have been used to investigate the… (more)

▼ Reaction – diffusion based tumor models have been used to explore tumor growth for the past 30 years. These models have been used to investigate the effects of various treatment options such as surgical resection, chemotherapy, and radiation therapy. These previous models have all focused only on dividing cell populations. In this work we will develop a reaction – diffusion model for radiation therapy treatment that includes three populations: (1) dividing cells that healthy and divide as normal; (2) doomed cells that have been irradiated and received lethal damage, but continue to divide for several generations before expiring; and (3) dead cells that have expired, but have not yet been removed from the tumor site thus contributing to the overall tumor volume. Section 1 will give an introductory overview of radiation physics, the radiobiology, and cellular mechanics necessary for the model. Section 2 will review previous diffusion models and lay the mathematical framework for the current model and the numerical methods needed to solve it. The current model is a system of partial differential equations that are solved using a Crank – Nicolson tri – diagonal matrix method. Section 3 will review the results of applying the model to both experimental rat data from historical literature as well as patient data from brain metastases treated with Gamma Knife stereotactic radiosurgery. Section 4 will use the model to investigate the effects of non – uniform dose distributions on the end volume of tumors treated with multi – fraction treatments. The biologically effective dose (BED) formula is generally used to calculate dose per fraction values for multiple – fraction treatments to ensure that they would have the same biological effect as a single – fraction treatment. This section will show that if the dose distribution is not uniform across the tumor, the standard BED formula does not satisfy this assumption and a new formula is developed to calculate dose per fraction values. Finally, Section 5 will apply the diffusion concept to the reoxygenation of a tumor site. A two – dimensional diffusion model for oxygen within a tumor is solved using an alternating direction implicit (ADI) Crank – Nicolson method. This 2D model will be used to determine the effect of the loss of oxygen input to the tumor site on the oxygen distribution within that tumor site. We intend for this extension of reaction – diffusion based tumor models to help drive improvement to treatment optimization by being able to accurately simulate near – term tumor response to radiation.

Subjects/Keywords: Crank-Nicolson; Diffusion equation; Mathematical model; Oxygen diffusion

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dahlman, E. (2019). Mathematical models and simulation of tumor growth, radiation response, and micro-environment. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/211744

Chicago Manual of Style (16^th Edition):

Dahlman, Erik. “Mathematical models and simulation of tumor growth, radiation response, and micro-environment.” 2019. Doctoral Dissertation, University of Minnesota. Accessed March 06, 2021. http://hdl.handle.net/11299/211744.

MLA Handbook (7^th Edition):

Dahlman, Erik. “Mathematical models and simulation of tumor growth, radiation response, and micro-environment.” 2019. Web. 06 Mar 2021.

Vancouver:

Dahlman E. Mathematical models and simulation of tumor growth, radiation response, and micro-environment. [Internet] [Doctoral dissertation]. University of Minnesota; 2019. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/11299/211744.

Council of Science Editors:

Dahlman E. Mathematical models and simulation of tumor growth, radiation response, and micro-environment. [Doctoral Dissertation]. University of Minnesota; 2019. Available from: http://hdl.handle.net/11299/211744

5. Luz, Hedhio Luiz Francisco da. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.

Degree: Mestrado, Física, 2008, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/ ;

►

No presente trabalho foi estudada a dinâmica de um sistema de muitas partículas no regime de temperaturas ultra-baixas. Realizamos um estudo dinâmico de sistemas condensados… (more)

▼

No presente trabalho foi estudada a dinâmica de um sistema de muitas partículas no regime de temperaturas ultra-baixas. Realizamos um estudo dinâmico de sistemas condensados bidimensionais em uma rede óptica não-linear em uma direção e também na presença de uma armadilha harmônica assimétrica. Investigamos alguns aspectos sobre a estabilização e propagação de sólitons em condensados de Bose-Einstein. O colapso da função de onda é evitado pela não-linearidade periódica dissipativa, no caso de um meio com campo de fundo positivo (com sistemas atômicos atrativos). A variação adiabática do comprimento de espalhamento de fundo leva a existência de sólitons de onda de matéria metaestáveis. Um sóliton dissipativo pode existir no meio atrativo bidimensional (2D) com uma não-linearidade periódica unidimensional (1D), quando um mecanismo de alimentação atômica é utilizado. Um sóliton estável pode existir no caso de condensados repulsivos, em um campo de fundo negativo, com uma armadilha harmônica em uma direção e uma rede óptica não-linear na outra direção. Os resultados inteiramente numéricos, para a equação de Gross-Pitaevskii 2D, confirmam as simulações da abordagem variacional.

In this work the dynamics of a system of many particles in a ultra-low temperature regime was studied. We performed a dynamic study of two-dimensional condensate systems into a nonlinear optical lattice in one direction and also in the presence of an asymmetrical harmonic trap. We investigated some aspects of the stabilization and spread of solitons in a Bose-Einstein condensate. In the case of positive background field media (with attractive atomic systems), the collapse of the wave-packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in an attractive bidimensional (2D) media with unidimensional (1D) periodic nonlinearity. In the case of repulsive condensates, with a negative background field, a stable soliton may exist when we have an harmonic trap in one direction and a nonlinear optical lattice in the other. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Advisors/Committee Members: Tomio, Lauro.

Subjects/Keywords: Bose-Einstein condensation; Condensação de Bose-Einstein; Crank-Nicolson; Crank-Nicolson; Equação de Gross-Pitaevskii; Gross-Pitaevskii equation; Numerical simulation.; Simulação numérica.; Solitons; Sólitons

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Luz, H. L. F. d. (2008). Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/ ;

Chicago Manual of Style (16^th Edition):

Luz, Hedhio Luiz Francisco da. “Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.” 2008. Masters Thesis, University of São Paulo. Accessed March 06, 2021. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/ ;.

MLA Handbook (7^th Edition):

Luz, Hedhio Luiz Francisco da. “Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo.” 2008. Web. 06 Mar 2021.

Vancouver:

Luz HLFd. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. [Internet] [Masters thesis]. University of São Paulo; 2008. [cited 2021 Mar 06]. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/ ;.

Council of Science Editors:

Luz HLFd. Sistemas não-lineares aplicados a condensados atômicos com interações dependentes do tempo. [Masters Thesis]. University of São Paulo; 2008. Available from: http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-095040/ ;

Universidade Estadual de Campinas

6. Carmona Tabares, Paulo Cesar, 1976-. Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove.

Degree: 2012, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307271

► Abstract: In this work, we built a mathematical model to evaluate existing conjectures about the impact that inorganic particulate material (sediment) has upon predominating benthic… (more)

Subjects/Keywords: Ecologia matemática; Equações diferenciais parciais; Galerkin, Métodos de; Crank-Nicolson, Método de; Simulação (Computadores); Mathematical ecology; Partial differential equations; Galerkin method; Crank¿Nicolson method; Computer Simulations

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Carmona Tabares, Paulo Cesar, 1. (2012). Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/307271

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Carmona Tabares, Paulo Cesar, 1976-. “Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove.” 2012. Thesis, Universidade Estadual de Campinas. Accessed March 06, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307271.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Carmona Tabares, Paulo Cesar, 1976-. “Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove.” 2012. Web. 06 Mar 2021.

Vancouver:

Carmona Tabares, Paulo Cesar 1. Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove. [Internet] [Thesis]. Universidade Estadual de Campinas; 2012. [cited 2021 Mar 06]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307271.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Carmona Tabares, Paulo Cesar 1. Impacto do sedimento sobre espécies que interagem = modelagem e simulações de bentos na Enseada Potter: Sediment impact upon interacting species : modeling and numerical simulation of benthos at Potter Cove. [Thesis]. Universidade Estadual de Campinas; 2012. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/307271

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

7. Lindqvist, Petter. Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar.

Degree: Environmental and Natural Resources Engineering, 2020, Luleå University of Technology

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79973

►

FDS (Fire Dynamics Simulator) använder en version av Navier-Stokes ekvationerna för att göra noggranna beräkningar av värme- och gastransport genom brandbelastade utrymmen. Utvecklarna av… (more)

▼

FDS (Fire Dynamics Simulator) använder en version av Navier-Stokes ekvationerna för att göra noggranna beräkningar av värme- och gastransport genom brandbelastade utrymmen. Utvecklarna av programmet arbetar kontinuerligt med att validera det allteftersom nya funktioner tillförs för att öka noggrannheten och bredda tillämpningsområdena. Väldigt lite av detta arbete fokuserar dock på FDS:s konduktionsmodell, den endimensionella Crank-Nicolson metoden. Det här examensarbetet ämnar därför undersöka noggrannheten i FDS:s konduktionsmodell genom jämförelse mot beräkningar med FEM (Finita elementmetoden). En FDS-modell skapades för att tillåta undersökning av en vägg och dess randvillkor med så liten påverkan från andra faktorer som möjligt. Detta för att skapa en kontrollerad omgivning som enkelt kunde replikeras i efterföljande FE-beräkningar av det konduktiva värmeflödet genom den solida obstruktionen. Tre väggar (10 cm betong, 20 cm betong och 1 mm stål) vardera med tre randvillkor (Exposed, Void och Insulated) utsattes för tre temperaturer (100 °C, 500 °C och 1000 °C) vilket ger 27 FDS simuleringar. Den adiabatiska yttemperaturen mättes i varje simulering och användes som indata till motsvarande FE-beräkningar. Resultatet påvisade inga signifikanta motsägelser vad gäller randvillkoren, med tillräcklig tid för termisk penetrering påverkade de den resulterande temperaturen som väntat. Undantaget var en mindre avvikelse i stålväggarna som utsattes för 100 °C och 500 °C med randvillkoren Exposed och Void där FDS aningen underskattade temperaturen relativt FE-beräkningarna. Gastemperaturerna i gridcellerna närmast väggen visade sig vara opålitliga. De tenderade att genomgå substantiella fluktuationer, troligen som ett resultat av hur FDS hanterar diskretiseringen av icke-solida volymer för Navier-Stokes beräkningarna. Dessa fluktuationer påverkade dock inte de resulterande solida temperaturerna eftersom medelgastemperaturen var korrekt. FDS påvisades även ha en tendens att aningen överskatta yttemperaturen under de första minuterna av simuleringarna relativt FE-beräkningarna. Temperaturerna från de två beräkningsmetoderna konvergerade dock efter några få minuter i samtliga tester. Dessa avvikelser ansågs ha för liten påverkan på de solida temperaturerna för att påvisa onoggrannhet i FDS. Därmed drogs slutsatsen att FDS:s beräkningar av temperaturer i solida material är tillräckligt noggranna inom dessa avgränsningar.

FDS (Fire Dynamics Simulator) uses a version of the Navier-Stokes equations to make accurate calculations of heat and gas flow through enclosures exposed to fire. The developers of FDS have, and continue to, validate it as new features get added in an attempt to increase its accuracy and broaden its potential applications. However, little of this effort is focused on FDS’ conductive heat transfer model, based on the one-dimensional Crank-Nicolson method. Thus, this study aims to test the accuracy of FDS’ conduction model by comparing it to calculations using FEM…

Subjects/Keywords: FDS; Fire Dynamics Simulator; FEM; Finite Element Method; Crank-Nicolson; validation; conduction; walls; FDS; Fire Dynamics Simulator; FEM; Finita elementmetoden; Crank-Nicolson; validering; konduktion; väggar; Civil Engineering; Samhällsbyggnadsteknik

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lindqvist, P. (2020). Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar. (Thesis). Luleå University of Technology. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79973

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Lindqvist, Petter. “Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar.” 2020. Thesis, Luleå University of Technology. Accessed March 06, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79973.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Lindqvist, Petter. “Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar.” 2020. Web. 06 Mar 2021.

Vancouver:

Lindqvist P. Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar. [Internet] [Thesis]. Luleå University of Technology; 2020. [cited 2021 Mar 06]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79973.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lindqvist P. Validering av solida temperaturer i FDS genom jämförelse mot FE-beräkningar. [Thesis]. Luleå University of Technology; 2020. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79973

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Ontario Institute of Technology

8. Bandola, Nicolas. Diffusion in inhomogenous media.

Degree: MSc, Modelling and Computational Science, 2010, University of Ontario Institute of Technology

URL: http://hdl.handle.net/10155/78

► This project considers the diffusion of water molecules through a cellular medium in which the cells are modeled by square compartments placed symmetrically in a… (more)

Subjects/Keywords: Crank-Nicolson scheme; Water molecule diffusion; Comsol Multiphysics; Apparent Diffusion Coefficient (ADC); Ischemia

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bandola, N. (2010). Diffusion in inhomogenous media. (Masters Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/78

Chicago Manual of Style (16^th Edition):

Bandola, Nicolas. “Diffusion in inhomogenous media.” 2010. Masters Thesis, University of Ontario Institute of Technology. Accessed March 06, 2021. http://hdl.handle.net/10155/78.

MLA Handbook (7^th Edition):

Bandola, Nicolas. “Diffusion in inhomogenous media.” 2010. Web. 06 Mar 2021.

Vancouver:

Bandola N. Diffusion in inhomogenous media. [Internet] [Masters thesis]. University of Ontario Institute of Technology; 2010. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10155/78.

Council of Science Editors:

Bandola N. Diffusion in inhomogenous media. [Masters Thesis]. University of Ontario Institute of Technology; 2010. Available from: http://hdl.handle.net/10155/78

Anna University

9. Kannan M. Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;.

Degree: 2014, Anna University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/15483

►

This thesis discusses the theoretical and numerical solutions of the magnetohydrodynamic effects on the free convective flow, past an impulsively started moving semi-infinite vertical cylinder,… (more)

▼

This thesis discusses the theoretical and numerical solutions of the magnetohydrodynamic effects on the free convective flow, past an impulsively started moving semi-infinite vertical cylinder, in the presence of heat and mass transfer with/without thermal radiation or chemical reaction and various boundary conditions. Initially, the cylinder and the fluid are of the same temperature and concentration. The governing equations of free convection are simplified by invoking the boundary layer at the Boussinesq s approximations. The governing equations are transformed into a dimensionless form, by using suitable non-dimensional quantities. The effects of the velocity, temperature and concentration fields in the transient and steady-state are studied for various parameters, like the magnetic field, radiation, chemical reaction and time, presented in the form of graphs and tables. The numerical solution of the magnetohydrodynamic effects on the unsteady natural convection flow of a viscous incompressible fluid past an impulsively started semi-infinite vertical cylinder in the presence of heat and mass transfer has been discussed for the boundary conditions of (i) temperature oscillation and (ii) uniform heat and mass flux. The stability of the finite difference scheme of the Crank-Nicolson type is analyzed, using the Von-Neumann technique. The numerical results are presented in the form of graphs for various values of the parameters. In order to ascertain the accuracy of the numerical results, the present studies are compared with the available theoretical solutions in the literature, and they are found to be in good agreement. The present work is more concerned with the transient part. The time taken to reach the steady state is observed for various values of parameters. The fluid considered in this study is air. The effects of the velocity, temperature and the concentration fields in the transient and steady state are studied. The local and average values of the skin-friction, Nusselt number and Sherwood number are

Advisors/Committee Members: Loganathan P.

Subjects/Keywords: Magnetohydrodynamic; Boussinesq s approximations; temperature oscillation; uniform heat; mass flux; Crank-Nicolson

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

M, K. (2014). Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;. (Thesis). Anna University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/15483

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

M, Kannan. “Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;.” 2014. Thesis, Anna University. Accessed March 06, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/15483.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

M, Kannan. “Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;.” 2014. Web. 06 Mar 2021.

Vancouver:

M K. Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;. [Internet] [Thesis]. Anna University; 2014. [cited 2021 Mar 06]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/15483.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

M K. Magnetohydrodynamic effects on the free convective flow over a moving vertical cylinder;. [Thesis]. Anna University; 2014. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/15483

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of South Carolina

10. Tatano, Rosalia. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.

Degree: MS, Mathematics, 2013, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/1613

► In this thesis we solve two-dimensional linear parabolic partial differential equations with pure Dirichelet boundary conditions, using the bilinear covolume-upwind finite volume method on… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; Crank-Nicolson; finite volume methods; linear parabolic PDE

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tatano, R. (2013). Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/1613

Chicago Manual of Style (16^th Edition):

Tatano, Rosalia. “Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.” 2013. Masters Thesis, University of South Carolina. Accessed March 06, 2021. https://scholarcommons.sc.edu/etd/1613.

MLA Handbook (7^th Edition):

Tatano, Rosalia. “Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.” 2013. Web. 06 Mar 2021.

Vancouver:

Tatano R. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. [Internet] [Masters thesis]. University of South Carolina; 2013. [cited 2021 Mar 06]. Available from: https://scholarcommons.sc.edu/etd/1613.

Council of Science Editors:

Tatano R. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. [Masters Thesis]. University of South Carolina; 2013. Available from: https://scholarcommons.sc.edu/etd/1613

Delft University of Technology

11. Lantsheer, M. (author). Tracking Free Surface Flows Using the Least Squares Spectral Element Method.

Degree: 2010, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:3512f664-92d0-464f-a692-41cc21e36f19

Aerospace Engineering Advisors/Committee Members: Bijl, H. (mentor), Gerritsma, M.I. (mentor).

Subjects/Keywords: Discretisation; Least Squares; Spectral Elements; Poisson; Crank-Nicolson

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lantsheer, M. (. (2010). Tracking Free Surface Flows Using the Least Squares Spectral Element Method. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:3512f664-92d0-464f-a692-41cc21e36f19

Chicago Manual of Style (16^th Edition):

Lantsheer, M (author). “Tracking Free Surface Flows Using the Least Squares Spectral Element Method.” 2010. Masters Thesis, Delft University of Technology. Accessed March 06, 2021. http://resolver.tudelft.nl/uuid:3512f664-92d0-464f-a692-41cc21e36f19.

MLA Handbook (7^th Edition):

Lantsheer, M (author). “Tracking Free Surface Flows Using the Least Squares Spectral Element Method.” 2010. Web. 06 Mar 2021.

Vancouver:

Lantsheer M(. Tracking Free Surface Flows Using the Least Squares Spectral Element Method. [Internet] [Masters thesis]. Delft University of Technology; 2010. [cited 2021 Mar 06]. Available from: http://resolver.tudelft.nl/uuid:3512f664-92d0-464f-a692-41cc21e36f19.

Council of Science Editors:

Lantsheer M(. Tracking Free Surface Flows Using the Least Squares Spectral Element Method. [Masters Thesis]. Delft University of Technology; 2010. Available from: http://resolver.tudelft.nl/uuid:3512f664-92d0-464f-a692-41cc21e36f19

12. Ay, Buket. Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri .

Degree: ESOGÜ, Fen Edebiyat Fakültesi, Matematik ve Bilgisayar Bilimleri, 2015, Eskisehir Osmangazi University

URL: http://hdl.handle.net/11684/1011

► Kısmi türevli diferensiyel denklemler temel doğa yasalarının matematiksel modellemesinde ve birçok problemin matematiksel analizinde ortaya çıkmaktadır. Bu tür denklemler lineer ve lineer olmayan kısmi türevli… (more)

Subjects/Keywords: Lineer Olmayan Kısmi Türevli Diferansiyel Denklemler; Regularised Long Wave (RLW) Denklemi; Burgers Denklemi; Crank-Nicolson; Trigonometrik Bspline; Subdomain Galerkin; Nonlinear Partial Differential Equations; Regularised Long Wave (RLW) Equation; Burgers’ Equation; Crank-Nicolson; Trigonometric B-spline; Subdomain Galerkin Method

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ay, B. (2015). Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri . (Thesis). Eskisehir Osmangazi University. Retrieved from http://hdl.handle.net/11684/1011

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ay, Buket. “Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri .” 2015. Thesis, Eskisehir Osmangazi University. Accessed March 06, 2021. http://hdl.handle.net/11684/1011.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ay, Buket. “Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri .” 2015. Web. 06 Mar 2021.

Vancouver:

Ay B. Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri . [Internet] [Thesis]. Eskisehir Osmangazi University; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/11684/1011.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ay B. Trigonometrik B-spline subdomain galerkin yöntemi ile zamana bağlı bir boyutlu lineer olmayan kısmi türevli diferensiyel denklemlerin yaklaşık çözümleri . [Thesis]. Eskisehir Osmangazi University; 2015. Available from: http://hdl.handle.net/11684/1011

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

North-West University

13. Joubert, Dominique. Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert .

Degree: 2013, North-West University

URL: http://hdl.handle.net/10394/10202

► The Black-Scholes model and its assumptions has endured its fair share of criticism. One problematic issue is the model’s assumption that market volatility is constant.… (more)

Subjects/Keywords: Early exercise boundary; Free boundary value problem; Linear complimentary problem; Crank-Nicolson finite difference method; rojected Over-Relaxation method (PSOR); Stochastic volatility; Heston stochastic volatility model; Vroeë uitoefengrens; Vrye grenswaardeprobleem; Liniêre komplimentêre probleem; Crank-Nicolson eindige differensiemetode; Geprojekteerde oorverslappingsmetode (PSOR); Stogastiese volatiliteit; Heston stogastiese volatiliteitsmodel

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Joubert, D. (2013). Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert . (Thesis). North-West University. Retrieved from http://hdl.handle.net/10394/10202

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Joubert, Dominique. “Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert .” 2013. Thesis, North-West University. Accessed March 06, 2021. http://hdl.handle.net/10394/10202.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Joubert, Dominique. “Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert .” 2013. Web. 06 Mar 2021.

Vancouver:

Joubert D. Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert . [Internet] [Thesis]. North-West University; 2013. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10394/10202.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Joubert D. Numerical methods for pricing American put options under stochastic volatility / Dominique Joubert . [Thesis]. North-West University; 2013. Available from: http://hdl.handle.net/10394/10202

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

14. Vergez, Guillaume. Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates.

Degree: Docteur es, Mathematiques, 2017, Normandie

URL: http://www.theses.fr/2017NORMR014

►

Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux… (more)

▼

Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux de Bose. Depuis lors, de nombreux physiciens,mathématiciens et numériciens se sont intéressés au condensat de Bose-Einstein et à son caractère superfluide. Nous proposons dans cette étude des méthodes numériques ainsi qu’un code informatique pour la simulation d’un condensat de Bose-Einstein en rotation. Le principal modèle mathématique décrivant ce phénomène physique est une équation de Schrödinger présentant une non-linéarité cubique,découverte en 1961 : l’équation de Gross-Pitaevskii (GP). En nous appuyant sur le logiciel FreeFem++,nous nous servons d’une discrétisation spatiale en éléments-finis pour résoudre numériquement cette équation. Une méthode d’adaptation du maillage à la solution et l’utilisation d’éléments-finis d’ordre deux nous permet de résoudre finement le problème et d’explorer des configurations complexes en deux ou trois dimensions d’espace. Pour sa version stationnaire, nous avons développé une méthode de gradient de Sobolev ou une méthode de point intérieur implémentée dans la librairie Ipopt. Pour sa version instationnaire, nous utilisons une méthode de Time-Splitting combinée à un schéma de Crank-Nicolson ou une méthode de relaxation. Afin d’étudier la stabilité dynamique et thermodynamique d’un état stationnaire, le modèle de Bogoliubov-de Gennes propose une linéarisation de l’équation de Gross-Pitaevskii autour de cet état. Nous avons élaboré une méthode permettant de résoudre ce système aux valeurs et vecteurs propres, basée sur un algorithme de Newton ainsi que sur la méthode d’Arnoldi implémentée dans la librairie Arpack.

The phenomenon of condensation of a boson gas when cooled to zero degrees Kelvin was described by Einstein in 1925 based on work by Bose. Since then, many physicists, mathematicians and digitizers have been interested in the Bose-Einstein condensate and its superfluidity. We propose in this study numerical methods as well as a computer code for the simulation of a rotating Bose-Einstein condensate.The main mathematical model describing this phenomenon is a Schrödinger equation with a cubic nonlinearity, discovered in 1961: the Gross-Pitaevskii (GP) equation. By using the software FreeFem++ and a finite elements spatial discretization we solve this equation numerically. The mesh adaptation to the solution and the use of finite elements of order two allow us to solve the problem finely and to explore complex configurations in two or three dimensions of space. For its stationary version, we have developed a Sobolev gradient method or an internal point method implemented in the Ipopt library. .For its unsteady version, we use a Time-Splitting method combined with a Crank-Nicolson scheme ora relaxation method. In order to study the dynamic and thermodynamic stability of a stationary state,the Bogoliubov-de Gennes model proposes a linearization of the Gross-Pitaevskii equation around this state. We have developed a method…

Advisors/Committee Members: Danaila, Ionut (thesis director), Hecht, Frédéric (thesis director).

Subjects/Keywords: Dir. mathematiques; FreeFem++; Ipopt; Gross-Pitaevskii; Bose-Einstein; Eléments finis; Adaptation de maillage; Méthode de splitting; Relaxation; Crank-Nicolson; Newton; Bogoliubov-de Gennes; Arpack; FreeFem++; Ipopt; Gross-Pitaevskii; Bose-Einstein; Finite elements; Mesh adaptivity; Splitting method; Relaxation; Crank-Nicolson; Newton; Bogoliubov-de Gennes; Arpack; 510

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Vergez, G. (2017). Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates. (Doctoral Dissertation). Normandie. Retrieved from http://www.theses.fr/2017NORMR014

Chicago Manual of Style (16^th Edition):

Vergez, Guillaume. “Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates.” 2017. Doctoral Dissertation, Normandie. Accessed March 06, 2021. http://www.theses.fr/2017NORMR014.

MLA Handbook (7^th Edition):

Vergez, Guillaume. “Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates.” 2017. Web. 06 Mar 2021.

Vancouver:

Vergez G. Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates. [Internet] [Doctoral dissertation]. Normandie; 2017. [cited 2021 Mar 06]. Available from: http://www.theses.fr/2017NORMR014.

Council of Science Editors:

Vergez G. Méthodes numériques avec des éléments finis adaptatifs pour la simulation de condensats de Bose-Einstein : Adaptive Finite-element Methods for the Numerical Simulation of Bose-Einstein Condensates. [Doctoral Dissertation]. Normandie; 2017. Available from: http://www.theses.fr/2017NORMR014

Universidade Estadual de Campinas

15. Ramírez Bernate, Carmen Alicia, 1976-. Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti".

Degree: 2017, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/331000

► Abstract: There are very traditional control techniques to combat the mosquito Aedes aegypti, transmitter of the virus of Dengue, Chikungunya and Zika. One of them… (more)

▼ Abstract: There are very traditional control techniques to combat the mosquito Aedes aegypti, transmitter of the virus of Dengue, Chikungunya and Zika. One of them is the chemical control through the use of insecticides, of very high consumption in recent years. However they have not proven to be many effective as a mechanism for controlling mosquitoes when they develop resistance. A new technique for the control of this mosquito consists of its modification genetics, giving rise to the sterile mosquito. A mating between wild female and sterile male produces eggs that will not hatch; with a large number of these males, crossbreeding will not produce new mosquitoes reducing the wild population. This is known as the sterile insect release technique (SIT) (BARLETT; STATEN, 1996). In this work, the behavior (increase or decrease) of the Aedes aegypti mosquito population in space is analyzed over the time, initially considering control by induced mortality caused by the use of larvicides and adulticides, which are modeled with variables parameters, applied in the aquatic and winged phases respectively. After this same behavior is analyzed once the sterile mosquito is released into an area with initial distribution of known wild population. Then appropriate combinations of these techniques are made an the efficiency of each is determined. For this, the model studied in (ESTEVA; YANG, 2005) is used, adding the advective and dispersive terms related to migration and geographics dispersion respectively. For the proposed model, the existence and uniqueness of weak and strong solutions are verified by applying he theorem studied in (BOTHE et al., 2017). In the numerical simulations the classical finite element method is used for the discretization of the spatial variable, the Crank-Nicolson method for the time variable and finally for the treatment of nonlinearities a predictor-corrector method is used. Subsequently, an analysis of the error and convergence is performed showing the good implementation of these methods. Finally, numerical simulations are presented, testing different control scenarios. It is verified that the dispersion parameter has a strong influence on the distribution of these mosquitoes and that the combined use of insecticides with sterile mosquitoes is an efficient strategy for vector control Advisors/Committee Members: UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP), Meyer, João Frederico da Costa Azevedo, 1947- (advisor), Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Ciência da Computação (institution), Programa de Pós-Graduação em Matemática Aplicada (nameofprogram), Yang, Hyun Mo (committee member), Barros, Laécio Carvalho de (committee member), Peixoto, Magda da Silva (committee member), Mistro, Diomar Cristina (committee member).

Subjects/Keywords: Equações diferenciais parciais - Soluções numéricas; Existência de solução (Equações diferenciais); Método dos elementos finitos; Crank-Nicolson, Método de; Aedes Aegypti - Controle; Método preditor-corretor; Inseticidas; Partial differential equations - Numerical solutions; Existence of solutions (Differential equations); Finite elements method; Crank-Nicolson method; Aedes aegypti - Control; Predictor-corrector methods; Insecticides

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ramírez Bernate, Carmen Alicia, 1. (2017). Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti". (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/331000

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ramírez Bernate, Carmen Alicia, 1976-. “Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti".” 2017. Thesis, Universidade Estadual de Campinas. Accessed March 06, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/331000.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ramírez Bernate, Carmen Alicia, 1976-. “Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti".” 2017. Web. 06 Mar 2021.

Vancouver:

Ramírez Bernate, Carmen Alicia 1. Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti". [Internet] [Thesis]. Universidade Estadual de Campinas; 2017. [cited 2021 Mar 06]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/331000.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ramírez Bernate, Carmen Alicia 1. Modelagem matemática e simulações computacionais de estratégias combinadas de combate a um inseto vetor : o caso do "Aedes aegypti": Mathematical modeling and numerical simulations of combined strategies for the elimination of a vector insect : the case of the "Aedes aegypti". [Thesis]. Universidade Estadual de Campinas; 2017. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/331000

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

16. Natalia Cristina Braga Arruda Alves da Silva. Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo.

Degree: 2006, Laboratório Nacional de Computação Científica

URL: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=46 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=47 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=48 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=49 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=50

►

Nesta dissertação apresenta-se a análise de métodos totalmente discretos, estabilizados espacialmente, para a resolução de problemas de transporte unidimensionais convectivos-difusivos-reativos, lineares e transientes que modelam… (more)

▼

Nesta dissertação apresenta-se a análise de métodos totalmente discretos, estabilizados espacialmente, para a resolução de problemas de transporte unidimensionais convectivos-difusivos-reativos, lineares e transientes que modelam o transporte de contaminantes radioativos com decaimento a uma taxa constante em um meio poroso saturado. O método de elementos finitos clássico de Galerkin é usado no espaço quando o problema de transporte é pura e/ou predominantemente difusivo, ao passo que quando a convecção domina, o método SUPG (Streamline Upwind Petrov-Galerkin) é utilizado. O método de elementos finitos é combinado a um esquema discreto de integração no tempo, os algoritmos trapezoidais generalizados. Observa-se que a solução aproximada pode apresentar oscilações espúrias quando o método de Crank-Nicolson é utilizado. São consideradas diversas metodologias propostas na literatura para amortecer tais oscilações. Como consequência da análise de estabilidade desenvolvida, uma nova condição de estabilidade é proposta.

This work deals with the stability analysis of the fully discrete transport problem obtained using a stable finite element method in space and the generalized trapeizoidal family of methods in time. Depeding on the range of parameters the Galerkin and the Streamline Upwind Petrov-Galerkin Methods are introduced. We evaluate the accuracy and stability properties of the methods. The sawtooth pattern in time is observed,caused by spurious higher modes when Crank-Nicolson method is used. We derive a stability analysis of the fully discrete method and investigate the techniques proposed in literature to damp oscillations. We propose a new stability condition to overcome the spurious modes. The proposed methodology is apllied to a one-dimensional contaminant transport problems in a saturated porous media that considers a radioactive contaminant decay at a constant rate.

Advisors/Committee Members: Sandra Mara Cardoso Malta, Augusto Cesar Noronha Rodrigues Galeão, Eduardo Gomes Dutra do Carmo, Rigoberto Gregório Sanabria de Castro, Regina Célia Cerqueira de Almeida.

Subjects/Keywords: ENGENHARIA DE TRANSPORTES; Métodos estabilizados; Estabilidade; Crank-Nicolson; Formulação semidiscreta; Teoria do transporte; Tranport theory; Análise numérica; Numerical analysis; Semidiscrete formulation; Crank-Nicolson; Stability methods; ENGENHARIA DE TRANSPORTES

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Silva, N. C. B. A. A. d. (2006). Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo. (Masters Thesis). Laboratório Nacional de Computação Científica. Retrieved from http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=46 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=47 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=48 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=49 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=50

Chicago Manual of Style (16^th Edition):

Silva, Natalia Cristina Braga Arruda Alves da. “Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo.” 2006. Masters Thesis, Laboratório Nacional de Computação Científica. Accessed March 06, 2021. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=46 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=47 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=48 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=49 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=50.

MLA Handbook (7^th Edition):

Silva, Natalia Cristina Braga Arruda Alves da. “Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo.” 2006. Web. 06 Mar 2021.

Vancouver:

Silva NCBAAd. Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo. [Internet] [Masters thesis]. Laboratório Nacional de Computação Científica; 2006. [cited 2021 Mar 06]. Available from: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=46 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=47 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=48 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=49 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=50.

Council of Science Editors:

Silva NCBAAd. Estabilidade temporal de formulações semi-discretas para problemas de transporte convectivo-difusivo-reativo. [Masters Thesis]. Laboratório Nacional de Computação Científica; 2006. Available from: http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=46 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=47 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=48 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=49 ; http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=50

Mississippi State University

17. Alwehebi, Aisha Abdullah. NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY.

Degree: PhD, Mathematics and Statistics, 2010, Mississippi State University

URL: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11182009-135917/ ;

► Most of PDE-based restoration models and their numerical realizations show a common drawback: loss of fine structures. In particular, they often introduce an unnecessary… (more)

Subjects/Keywords: Crank-Nicolson (CN) alternating direction implicit; equalized net diffusion; Rician distribution; Gaussian distribution; Magnetic resonance imaging (MRI); PDE based denoising models

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Alwehebi, A. A. (2010). NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY. (Doctoral Dissertation). Mississippi State University. Retrieved from http://sun.library.msstate.edu/ETD-db/theses/available/etd-11182009-135917/ ;

Chicago Manual of Style (16^th Edition):

Alwehebi, Aisha Abdullah. “NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY.” 2010. Doctoral Dissertation, Mississippi State University. Accessed March 06, 2021. http://sun.library.msstate.edu/ETD-db/theses/available/etd-11182009-135917/ ;.

MLA Handbook (7^th Edition):

Alwehebi, Aisha Abdullah. “NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY.” 2010. Web. 06 Mar 2021.

Vancouver:

Alwehebi AA. NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY. [Internet] [Doctoral dissertation]. Mississippi State University; 2010. [cited 2021 Mar 06]. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11182009-135917/ ;.

Council of Science Editors:

Alwehebi AA. NOISE CHARACTERISTICS AND EDGE-ENHANCING DENOISERS FOR THE MAGNITUDE MRI IMAGERY. [Doctoral Dissertation]. Mississippi State University; 2010. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-11182009-135917/ ;

18. FORERO VARELA, PAOLA. Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas .

Degree: 2013, Universidad de los Andes

URL: https://documentodegrado.uniandes.edu.co/documentos/7899.pdf

► En este artículo presentamos la valoración de un nuevo contrato de financiación de la educación superior, denominado contrato educativo de financiación dual (CED). Este contrato… (more)

Subjects/Keywords: Financiación de la Educación Superior; Becas Académicas; Contratos de Capital Humano; Opciones Exóticas; Crank Nicolson.

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

FORERO VARELA, P. (2013). Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas . (Thesis). Universidad de los Andes. Retrieved from https://documentodegrado.uniandes.edu.co/documentos/7899.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

FORERO VARELA, PAOLA. “Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas .” 2013. Thesis, Universidad de los Andes. Accessed March 06, 2021. https://documentodegrado.uniandes.edu.co/documentos/7899.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

FORERO VARELA, PAOLA. “Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas .” 2013. Web. 06 Mar 2021.

Vancouver:

FORERO VARELA P. Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas . [Internet] [Thesis]. Universidad de los Andes; 2013. [cited 2021 Mar 06]. Available from: https://documentodegrado.uniandes.edu.co/documentos/7899.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

FORERO VARELA P. Valoración de un Nuevo Contrato para la Financiación de la Educación Superior a través de Opciones Financieras Exóticas . [Thesis]. Universidad de los Andes; 2013. Available from: https://documentodegrado.uniandes.edu.co/documentos/7899.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Arizona

19. Espinola Rocha, Jesus Adrian. Short-time Asymptotic Analysis of the Manakov System .

Degree: 2006, University of Arizona

URL: http://hdl.handle.net/10150/195734

► The Manakov system appears in the physics of optical fibers, as well as in quantum mechanics, as multi-component versions of the Nonlinear Schrödinger and the… (more)

Subjects/Keywords: Integrable systems; asymptotic analysis; Solitons; Riemann-Hilbert Problems; Inverse Scattering Transform; Linearized Crank-Nicolson.

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Espinola Rocha, J. A. (2006). Short-time Asymptotic Analysis of the Manakov System . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/195734

Chicago Manual of Style (16^th Edition):

Espinola Rocha, Jesus Adrian. “Short-time Asymptotic Analysis of the Manakov System .” 2006. Doctoral Dissertation, University of Arizona. Accessed March 06, 2021. http://hdl.handle.net/10150/195734.

MLA Handbook (7^th Edition):

Espinola Rocha, Jesus Adrian. “Short-time Asymptotic Analysis of the Manakov System .” 2006. Web. 06 Mar 2021.

Vancouver:

Espinola Rocha JA. Short-time Asymptotic Analysis of the Manakov System . [Internet] [Doctoral dissertation]. University of Arizona; 2006. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10150/195734.

Council of Science Editors:

Espinola Rocha JA. Short-time Asymptotic Analysis of the Manakov System . [Doctoral Dissertation]. University of Arizona; 2006. Available from: http://hdl.handle.net/10150/195734

University of Maryland

20. Webster, Robert Dale. PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA.

Degree: Fire Protection Engineering, 2009, University of Maryland

URL: http://hdl.handle.net/1903/10004

► This study examines the ability of a stochastic hill-climber algorithm to develop an input parameter set to a finite difference one-dimensional model of transient conduction… (more)

Subjects/Keywords: Engineering, General; Engineering, Mechanical; Engineering, Materials Science; Crank-Nicolson; Fire; Genetic; modeling; optimization; Pyrolysis

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Webster, R. D. (2009). PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/10004

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Webster, Robert Dale. “PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA.” 2009. Thesis, University of Maryland. Accessed March 06, 2021. http://hdl.handle.net/1903/10004.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Webster, Robert Dale. “PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA.” 2009. Web. 06 Mar 2021.

Vancouver:

Webster RD. PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA. [Internet] [Thesis]. University of Maryland; 2009. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1903/10004.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Webster RD. PYROLYSIS MODEL PARAMETER OPTIMIZATION USING A CUSTOMIZED STOCHASTIC HILL-CLIMBER ALGORITHM AND BENCH SCALE FIRE TEST DATA. [Thesis]. University of Maryland; 2009. Available from: http://hdl.handle.net/1903/10004

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

21. Rouf, Hasan. Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media.

Degree: 2010, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:83291

► The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposedby the Courant–Friedrich–Lewy (CFL)… (more)

▼ The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposedby the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is agrowing interest in overcoming this limitation by employing unconditionally stableFDTD methods for which time-step and space-step can be independentlychosen. Unconditionally stable Crank Nicolson method has not been widely usedin time domain electromagnetics despite its high accuracy and low anisotropy.There has been no work on the Crank Nicolson FDTD (CN–FDTD) method forfrequency dependent medium.In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debyematerials is incorporated into the CN–FDTD method by means of an auxiliarydifferential formulation. In order to provide a convenient and straightforwardalgorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit.The proposed method yields a sparse system of linear equations which canbe solved by direct or iterative methods, but numerical experiments demonstratethat for large problems of practical importance iterative solvers are to be used.The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorateswith the increase of the time-step, making the solution time longer. Selectionof the matrix solver to handle the FD–CN–FDTD sparse system is crucial tofully harness the advantages of using larger time-step, because the computationalcosts associated with the solver must be kept as low as possible. Two best–knowniterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and GeneralisedMinimal Residual (GMRES), are extensively studied in terms of the number ofiteration requirements for convergence, CPU time and memory requirements.BiCGStab outperforms GMRES in every aspect. Many of these findings do notmatch with the existing literature on frequency–independent CN–FDTD methodand the possible reasons for this are pointed out.The proposed method is coded in Fortran and major implementation techniquesof the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model ofthe human body is developed in the FD–CN–FDTD method and numerical simulationof the electromagnetic wave propagation inside the human head is shown.Finally, this thesis presents a new method modifying the frequency dependentalternating direction implicit FDTD (FD–ADI–FDTD) method. Although theADI–FDTD method provides a computationally affordable approximation of theCN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTDmethod which may become severe for some practical applications. The modifiedFD–ADI–FDTD method can improve the accuracy of the normal FD–ADI–FDTDmethod… Advisors/Committee Members: Costen, Fumie.

Subjects/Keywords: Finite difference time domain (FDTD) method; Crank Nicolson method; Alternating direction implicit (ADI)-FDTD method; Frequency dependent materials; Sparse matrix solvers; Bioelectromagnetics

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rouf, H. (2010). Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:83291

Chicago Manual of Style (16^th Edition):

Rouf, Hasan. “Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media.” 2010. Doctoral Dissertation, University of Manchester. Accessed March 06, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:83291.

MLA Handbook (7^th Edition):

Rouf, Hasan. “Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media.” 2010. Web. 06 Mar 2021.

Vancouver:

Rouf H. Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media. [Internet] [Doctoral dissertation]. University of Manchester; 2010. [cited 2021 Mar 06]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:83291.

Council of Science Editors:

Rouf H. Unconditionally Stable Finite Difference Time Domain Methods for Frequency Dependent Media. [Doctoral Dissertation]. University of Manchester; 2010. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:83291

University of Manchester

22. Rouf, Hasan. Unconditionally stable finite difference time domain methods for frequency dependent media.

Degree: PhD, 2010, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/unconditionally-stable-finite-difference-time-domain-methods-for-frequency-dependent-media(50e4adf1-d1e4-4ad2-ab2d-70188fb8b7b6).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664533

► The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy… (more)

▼ The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. There has been no work on the Crank Nicolson FDTD (CN–FDTD) method for frequency dependent medium. In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debye materials is incorporated into the CN–FDTD method by means of an auxiliary differential formulation. In order to provide a convenient and straightforward algorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit. The proposed method yields a sparse system of linear equations which can be solved by direct or iterative methods, but numerical experiments demonstrate that for large problems of practical importance iterative solvers are to be used. The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorates with the increase of the time-step, making the solution time longer. Selection of the matrix solver to handle the FD–CN–FDTD sparse system is crucial to fully harness the advantages of using larger time-step, because the computational costs associated with the solver must be kept as low as possible. Two best–known iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), are extensively studied in terms of the number of iteration requirements for convergence, CPU time and memory requirements. BiCGStab outperforms GMRES in every aspect. Many of these findings do not match with the existing literature on frequency–independent CN–FDTD method and the possible reasons for this are pointed out. The proposed method is coded in Fortran and major implementation techniques of the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model of the human body is developed in the FD–CN–FDTD method and numerical simulation of the electromagnetic wave propagation inside the human head is shown. Finally, this thesis presents a new method modifying the frequency dependent alternating direction implicit FDTD (FD–ADI–FDTD) method. Although the ADI–FDTD method provides a computationally affordable approximation of the CN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTD method which may become severe for some practical applications. The modified FD–ADI–FDTD method can improve the accuracy of…

Subjects/Keywords: 621.381; Finite difference time domain (FDTD) method; Crank Nicolson method; Alternating direction implicit (ADI)-FDTD method; Frequency dependent materials; Sparse matrix solvers; Bioelectromagnetics

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rouf, H. (2010). Unconditionally stable finite difference time domain methods for frequency dependent media. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/unconditionally-stable-finite-difference-time-domain-methods-for-frequency-dependent-media(50e4adf1-d1e4-4ad2-ab2d-70188fb8b7b6).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664533

Chicago Manual of Style (16^th Edition):

Rouf, Hasan. “Unconditionally stable finite difference time domain methods for frequency dependent media.” 2010. Doctoral Dissertation, University of Manchester. Accessed March 06, 2021. https://www.research.manchester.ac.uk/portal/en/theses/unconditionally-stable-finite-difference-time-domain-methods-for-frequency-dependent-media(50e4adf1-d1e4-4ad2-ab2d-70188fb8b7b6).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664533.

MLA Handbook (7^th Edition):

Rouf, Hasan. “Unconditionally stable finite difference time domain methods for frequency dependent media.” 2010. Web. 06 Mar 2021.

Vancouver:

Rouf H. Unconditionally stable finite difference time domain methods for frequency dependent media. [Internet] [Doctoral dissertation]. University of Manchester; 2010. [cited 2021 Mar 06]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/unconditionally-stable-finite-difference-time-domain-methods-for-frequency-dependent-media(50e4adf1-d1e4-4ad2-ab2d-70188fb8b7b6).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664533.

Council of Science Editors:

Rouf H. Unconditionally stable finite difference time domain methods for frequency dependent media. [Doctoral Dissertation]. University of Manchester; 2010. Available from: https://www.research.manchester.ac.uk/portal/en/theses/unconditionally-stable-finite-difference-time-domain-methods-for-frequency-dependent-media(50e4adf1-d1e4-4ad2-ab2d-70188fb8b7b6).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664533

Georgia Tech

23. Carnevale, Kevin A. Finite-Difference Model of Cell Dehydration During Cryopreservation.

Degree: MS, Mechanical Engineering, 2004, Georgia Tech

URL: http://hdl.handle.net/1853/7258

► A numerical model for describing the kinetics of intracellular water transport during cryopreservation was developed. As ice is formed outside the cell, depleting the extracellular… (more)

Subjects/Keywords: Cryobiology; Cryopreservation; Membrane permeability; Vitrification; Membrane-limited water transport; Diffusion-limited water transport; Crank-Nicolson; Biot number; Peclet number; Dimensional analysis; Cell dehydration; Mathematical models; Finite differences

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Carnevale, K. A. (2004). Finite-Difference Model of Cell Dehydration During Cryopreservation. (Masters Thesis). Georgia Tech. Retrieved from http://hdl.handle.net/1853/7258

Chicago Manual of Style (16^th Edition):

Carnevale, Kevin A. “Finite-Difference Model of Cell Dehydration During Cryopreservation.” 2004. Masters Thesis, Georgia Tech. Accessed March 06, 2021. http://hdl.handle.net/1853/7258.

MLA Handbook (7^th Edition):

Carnevale, Kevin A. “Finite-Difference Model of Cell Dehydration During Cryopreservation.” 2004. Web. 06 Mar 2021.

Vancouver:

Carnevale KA. Finite-Difference Model of Cell Dehydration During Cryopreservation. [Internet] [Masters thesis]. Georgia Tech; 2004. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/1853/7258.

Council of Science Editors:

Carnevale KA. Finite-Difference Model of Cell Dehydration During Cryopreservation. [Masters Thesis]. Georgia Tech; 2004. Available from: http://hdl.handle.net/1853/7258

24. Burbey, Thomas J. A finite-difference model of three-dimensional granular displacement.

Degree: 1994, University of Nevada – Reno

URL: http://hdl.handle.net/11714/1163

► A three-dimensional finite-difference numerical model has been developed using the displacement field of solids as the unknown principal variable allowing for the simulation of granular… (more)

Subjects/Keywords: hydrology; modeling; numerical model; ground-water flow model; homogeneous aquifers; confined aquifers; unconfined; heterogeneous; vectors; Crank-Nicolson; Chebyshev; wells; boundary conditions; granular movement; finite-difference; Mackay Science Project; groundwater flow – models; aquifers; Darcy's Law

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Burbey, T. J. (1994). A finite-difference model of three-dimensional granular displacement. (Thesis). University of Nevada – Reno. Retrieved from http://hdl.handle.net/11714/1163

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Burbey, Thomas J. “A finite-difference model of three-dimensional granular displacement.” 1994. Thesis, University of Nevada – Reno. Accessed March 06, 2021. http://hdl.handle.net/11714/1163.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Burbey, Thomas J. “A finite-difference model of three-dimensional granular displacement.” 1994. Web. 06 Mar 2021.

Vancouver:

Burbey TJ. A finite-difference model of three-dimensional granular displacement. [Internet] [Thesis]. University of Nevada – Reno; 1994. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/11714/1163.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Burbey TJ. A finite-difference model of three-dimensional granular displacement. [Thesis]. University of Nevada – Reno; 1994. Available from: http://hdl.handle.net/11714/1163

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

25. Σφυράκης, Χρυσοβαλάντης. Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών.

Degree: 2008, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/23676

►

In this Ph.D. thesis, we solve numerically a phase field model describing the phase change of tow materials (e.g. solidification) in tow space dimensions, due… (more)

▼

In this Ph.D. thesis, we solve numerically a phase field model describing the phase change of tow materials (e.g. solidification) in tow space dimensions, due to McFadden, Wheeler, Sekerka, Wang. We seek two smooth functions, the phase indicator function ..., and the temperature ... These are defined for ... ...are known function of there are arguments Α is a 2 ... 2 matrix of function that depend an θ, and is given by...where ... is appropriate trigonometric function of ... Since the model is nonlinear and does not have in general closed form solutions, we solve it by numerical methods. We was finite difference schemes, for example the forward Euler method for the system p.d.e. and the Crank-Nicolson-Alternating Direction Implicit method for the send. In additions we present another finite difference method that uses the Crank- Nicolson-ADI scheme in both equations. For these numerical schemes we prove rigorous errors estimates and stability. For the fast solution of the scheme we development parallel methods which may be implemented in 1, 2, 4 processors and analyzed the efficiency of the parallel algorithm on such computing environment. Finally, we present the results of numerical experiment with these schemes that shows the motion of the interface between the two phases of the method and the onset of dendrite formation

Σε αυτή τη διδακτορική διατριβή επιλύουμε αριθμητικά ένα μοντέλο πεδίου φάσης για προβλήματα αλλαγής φάσης υλικών σε δύο χωρικές διαστάσεις που οφείλεται στους McFadden, Wheeler, Sekerka, Wang. Ζητούμε δύο αρκετά ομαλές συναρτήσεις, την συνάρτηση φάσης και τις θερμοκρασίας. Αυτές ορίζονται για ..., όπου ... είναι γνωστές συναρτήσεις και ο Α είναι ένας 2 2 πίνακας συναρτήσεων που εξαρτώνται από το θ, της μορφής ... όπου το ... είναι κατάλληλη τριγωνομετρική συνάρτηση του ... Δεδομένου ότι το μοντέλο είναι μη γραμμικό, και δεν έχει γενικά αναλυτική λύση, καταφεύγουμε στην επίλυση με αριθμητικές μεθόδους. Για την αριθμητική επίλυση χρησιμοποιούμε μεθόδους πεπερασμένων διαφορών όπως η άμεση μέθοδος Euler για την πρώτη εξίσωση και η μέθοδος Crank-Nicolson-Εναλασσομένων Κατευθύνσεων (ADI) για την δεύτερη. Επίσης παρουσιάζουμε μια δεύτερη αριθμητική μέθοδο πεπερασμένων διαφορών που επιλύει και τις δύο εξισώσεις του συστήματός με την μέθοδο Crank-Nicolson-Εναλασσομένων Κατευθύνσεων (ADI). Για τις παραπάνω αριθμητικές τεχνικές αποδείξαμε τόσο την ευστάθεια όσο και τη σύγκλισή τους. Για την ταχύτερη υλοποίηση των αλγορίθμων αναπτύξαμε παράλληλα σχήματα που μπορούν να επιλυθούν ταυτόχρονα σε 1, 2 ή 4 επεξεργαστές, και αναλύσαμε την απόδοση των παράλληλων αλγορίθμων σε τέτοια υπολογιστικά προβλήματα. Τέλος παρουσιάζουμε αποτελέσματα αριθμητικών πειραμάτων που δείχνουν την κίνηση της διεπιφάνειας κατά την αλλαγή φάσης του μετώπου και την έναρξη δημιουργίας δενδριτών

Subjects/Keywords: Μαθηματικά, Αριθμητικά μοντέλα; Αλλαγής φάσης υλικών; Παραβολικό σύστημα αρχικών και συνοριακών συνθηκών; Μέθοδος εναλλασσομένων κατευθύνσεων; Ανάδρομη Euler-Crank-Nicolson; Ύπαρξη λύσεων της μεθόδου διαφορών; Ευστάθεια, Εκτίμηση σφάλματος; Αλγόριθμοι, Παράλληλοι; Mathematics, Numerical models; Change phase materials; Parabolic system of initial and boundary conditions; Alternate Direction Implicit (ADI) method; Backward Euler-Crank-Nicolson; Existence of solutions of method fine deferens; Stability, Error estimat; Parallel algorithms

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Σφυράκης, . �. (2008). Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/23676

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Σφυράκης, Χρυσοβαλάντης. “Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών.” 2008. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed March 06, 2021. http://hdl.handle.net/10442/hedi/23676.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Σφυράκης, Χρυσοβαλάντης. “Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών.” 2008. Web. 06 Mar 2021.

Vancouver:

Σφυράκης �. Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2008. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10442/hedi/23676.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Σφυράκης �. Μαθηματικά και αριθμητικά μοντέλα για προβλήματα αλλαγής φάσης υλικών. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2008. Available from: http://hdl.handle.net/10442/hedi/23676

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Santana, Nilmar Bispo, 1986-. Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers.

Degree: 2019, Universidade Estadual de Campinas

URL: http://repositorio.unicamp.br/jspui/handle/REPOSIP/334399

► Abstract: In this work we propose a model with partial differential equation coupled to fuzzy parameters to study the dispersion of a pollution in a… (more)

Subjects/Keywords: Equação de difusão-advecção; Sistemas de controle biológico; Água - Qualidade - Medição - Métodos estatísticos; Água - Controle de qualidade; Sistemas fuzzy; Crank-Nicolson, Método de; Método dos elementos finitos; Diffusion-advection equation; Biological control systems; Water - Quality - Measurement - Statistical methods; Water quality management; Fuzzy systems; Crank-Nicolson method; Finite element method

10 more images…

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Santana, Nilmar Bispo, 1. (2019). Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers. (Thesis). Universidade Estadual de Campinas. Retrieved from http://repositorio.unicamp.br/jspui/handle/REPOSIP/334399

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Santana, Nilmar Bispo, 1986-. “Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers.” 2019. Thesis, Universidade Estadual de Campinas. Accessed March 06, 2021. http://repositorio.unicamp.br/jspui/handle/REPOSIP/334399.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Santana, Nilmar Bispo, 1986-. “Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers.” 2019. Web. 06 Mar 2021.

Vancouver:

Santana, Nilmar Bispo 1. Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers. [Internet] [Thesis]. Universidade Estadual de Campinas; 2019. [cited 2021 Mar 06]. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/334399.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Santana, Nilmar Bispo 1. Estudo da dispersão de poluentes na lagoa da Pampulha utilizando equações diferenciais parciais acoplada a controladores fuzzy: Study of pollutant dispersion in Pampulha lagoon using partial differential equations coupled to fuzzy controllers. [Thesis]. Universidade Estadual de Campinas; 2019. Available from: http://repositorio.unicamp.br/jspui/handle/REPOSIP/334399

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Torabi Ziaratgahi, Saeed. Efficient Numerical Methods for Heart Simulation.

Degree: 2015, University of Saskatchewan

URL: http://hdl.handle.net/10388/ETD-2015-04-2038

► The heart is one the most important organs in the human body and many other live creatures. The electrical activity in the heart controls the… (more)

▼ The heart is one the most important organs in the human body and many other live creatures. The electrical activity in the heart controls the heart function, and many heart diseases are linked to the abnormalities in the electrical activity in the heart. Mathematical equations and computer simulation can be used to model the electrical activity in the heart. The heart models are challenging to solve because of the complexity of the models and the huge size of the problems. Several cell models have been proposed to model the electrical activity in a single heart cell. These models must be coupled with a heart model to model the electrical activity in the entire heart. The bidomain model is a popular model to simulate the propagation of electricity in myocardial tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing the electrical activity at the cellular scale and a system of partial differential equations (PDEs) describing propagation of electricity at the tissue scale. Because of this multi-scale, ODE/PDE structure of the model, splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical methods. First, we need to solve the problem at the cellular scale using ODE solvers. One of the most popular methods to solve the ODEs is known as the Rush-Larsen (RL) method. Its popularity stems from its improved stability over integrators such as the forward Euler (FE) method along with its easy implementation. The RL method partitions the ODEs into two sets: one for the gating variables, which are treated by an exponential integrator, and another for the remaining equations, which are treated by the FE method. The success of the RL method can be understood in terms of its relatively good stability when treating the gating variables. However, this feature would not be expected to be of benefit on cell models for which the stiffness is not captured by the gating equations. We demonstrate that this is indeed the case on a number of stiff cell models. We further propose a new partitioned method based on the combination of a first-order generalization of the RL method with the FE method. This new method leads to simulations of stiff cell models that are often one or two orders of magnitude faster than the original RL method. After solving the ODEs, we need to use bidomain solvers to solve the bidomain model. Two well-known, first-order time-integration methods for solving the bidomain model are the semi-implicit method and the Godunov operator-splitting method. Both methods decouple the numerical procedure at the cellular scale from that at the tissue scale but in slightly different ways. The methods are analyzed in terms of their accuracy, and their relative performance is compared on one-, two-, and three-dimensional test cases. As suggested by the analysis, the test cases show that the Godunov method is significantly faster than the semi-implicit method for the same level of accuracy, specifically, between 5 and 15 times… Advisors/Committee Members: Spiteri, Raymond J., Sowa, Artur P., Patrick, George, Rice, Jeremy.

Subjects/Keywords: partitioned methods; efficient numerical methods; simulation of electrophysiological models; Rush-Larsen method; exponential integrator; ordinary differential equations; stiffness; bidomain model; operator splitting; Godunov method; semi-implicit method; unphysical oscillations; Crank-Nicolson method; SDIRK method; L-stability

…RRMS SDIRK SI TT Backward Euler Crank–Nicolson Differential-Algebraic Equation FitzHugh… …integrated in time with the Crank–Nicolson (CN) method. This method has also been used to… …amplification factors for the Cranck–Nicolson and SDIRK2 methods. 8 Chapter 2 Background In this…

1 more image…

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Torabi Ziaratgahi, S. (2015). Efficient Numerical Methods for Heart Simulation. (Thesis). University of Saskatchewan. Retrieved from http://hdl.handle.net/10388/ETD-2015-04-2038

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Torabi Ziaratgahi, Saeed. “Efficient Numerical Methods for Heart Simulation.” 2015. Thesis, University of Saskatchewan. Accessed March 06, 2021. http://hdl.handle.net/10388/ETD-2015-04-2038.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Torabi Ziaratgahi, Saeed. “Efficient Numerical Methods for Heart Simulation.” 2015. Web. 06 Mar 2021.

Vancouver:

Torabi Ziaratgahi S. Efficient Numerical Methods for Heart Simulation. [Internet] [Thesis]. University of Saskatchewan; 2015. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10388/ETD-2015-04-2038.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Torabi Ziaratgahi S. Efficient Numerical Methods for Heart Simulation. [Thesis]. University of Saskatchewan; 2015. Available from: http://hdl.handle.net/10388/ETD-2015-04-2038

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://hdl.handle.net/2003/29239

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan.

Subjects/Keywords: Block-Glätter; Block smoother; CFD; Crank-Nicolson; Crystal growth; Czochralski; Distributed Control; Edge-oriented stabilisation; Elliptic; Elliptisch; EOJ stabilisation; EOJ Stabilisierung; FEAT; FEATFLOW; Finite Elemente; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Hierarchisch; Hierarchisches Lösungskonzept; Inexact Newton; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Inverse Problems; Kantenbasierte Stabilisierung; KKT system; Kristallwachstum; Krylov; Large-Scale; linear complexity; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithic; Monolithisch; Multigrid; Multigrid-Krylov; Multilevel; Navier-Stokes; Nichtparametrische Finite Elemente; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimierung; Optimisation; Optimization; PDE Constraints; Raum-Zeit; saddle point; SAND; Sattelpunkt; Schur complement preconditioning; Schurkomplement-Vorkonditionierer; Space-time; SQP; Stokes; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; 510

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Thesis). Technische Universität Dortmund. Retrieved from http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Thesis, Technische Universität Dortmund. Accessed March 06, 2021. http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 06 Mar 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Thesis]. Technische Universität Dortmund; 2011. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/2003/29239.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Thesis]. Technische Universität Dortmund; 2011. Available from: http://hdl.handle.net/2003/29239

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

29. Αντωνοπούλου, Δήμητρα. Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων.

Degree: 2006, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/20913

Subjects/Keywords: Παραβολική εξίσωση σε μεταβλητό πυθμένα; Αλλαγή μεταβλητών; Πρόβλημα στις 2 και 3 διαστάσεις; Συνοριακές συνθήκες; Μέθοδοι πεπερασμένων στοιχείων; Εκτιμήσεις σφαλμάτων; Διακριτά - ημιδιακριτά σχήματα; Ασυνεχή ως προς το χρόνο πεπερασμένα στοχεία; Dirichzet neumann abrahamsson and kreiss; Schrodinger equation; Crank Nicolson scheme; Galerkin methods; A priori error estimations; Finite elements method; Space - time discontinuous methods; Numerical experiments - QMR method; Parabolic approximatons

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Αντωνοπούλου, . �. (2006). Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/20913

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Αντωνοπούλου, Δήμητρα. “Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων.” 2006. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed March 06, 2021. http://hdl.handle.net/10442/hedi/20913.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Αντωνοπούλου, Δήμητρα. “Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων.” 2006. Web. 06 Mar 2021.

Vancouver:

Αντωνοπούλου �. Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2006. [cited 2021 Mar 06]. Available from: http://hdl.handle.net/10442/hedi/20913.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Αντωνοπούλου �. Θεωρία και αριθμητική ανάλυση των παραβολικών προσεγγίσεων. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2006. Available from: http://hdl.handle.net/10442/hedi/20913

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

30. Köster, Michael. A Hierarchical Flow Solver for Optimisation with PDE Constraints.

Degree: 2011, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-6950

► Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt… (more)

▼ Active flow control plays a central role in many industrial applications such as e.g. control of crystal growth processes, where the flow in the melt has a significant impact on the quality of the crystal. Optimal control of the flow by electro-magnetic fields and/or boundary temperatures leads to optimisation problems with PDE constraints, which are frequently governed by the time-dependent Navier-Stokes equations. The mathematical formulation is a minimisation problem with PDE constraints. By exploiting the special structure of the first order necessary optimality conditions, the so called Karush-Kuhn-Tucker (KKT)-system, this thesis develops a special hierarchical solution approach for such equations, based on the distributed control of the Stokes – and Navier – Stokes. The numerical costs for solving the optimisation problem are only about 20-50 times higher than a pure forward simulation, independent of the refinement level. Utilising modern multigrid techniques in space, it is possible to solve a forward simulation with optimal complexity, i.e., an appropriate solver for a forward simulation needs O(N) operations, N denoting the total number of unknowns for a given computational mesh in space and time. Such solvers typically apply appropriate multigrid techniques for the linear subproblems in space. As a consequence, the developed solution approach for the optimal control problem has complexity O(N) as well. This is achieved by a combination of a space-time Newton approach for the nonlinearity and a monolithic space-time multigrid approach for 'global' linear subproblems. A second inner monolithic multigrid method is applied for subproblems in space, utilising local Pressure-Schur complement techniques to treat the saddle-point structure. The numerical complexity of this algorithm distinguishes this approach from adjoint-based steepest descent methods used to solve optimisation problems in many practical applications, which in general do not satisfy this complexity requirement. Advisors/Committee Members: Turek, Stefan (advisor), Meyer, Christian (referee).

Subjects/Keywords: Block-Glätter; Czochralski; Elliptisch; EOJ Stabilisierung; Finite Elemente; Hierarchisch; Hierarchisches Lösungskonzept; Inexaktes Newton-Verfahren; Instationär; Inverse Probleme; Kantenbasierte Stabilisierung; Kristallwachstum; Krylov; lineare Komplexität; Mehrgitter; Mehrgitter-Krylov; Monolithisch; Navier-Stokes; Nichtparametrische Finite Elemente; Optimierung; Raum-Zeit; Sattelpunkt; Schurkomplement-Vorkonditionierer; Stokes; Unstrukturierte Gitter; Vanka; Verteilte Kontrolle; Wärmeleitung; Wärmeleitungsgleichung; Block smoother; CFD; Crank-Nicolson; Crystal growth; Distributed Control; Edge-oriented stabilisation; Elliptic; EOJ stabilisation; FEAT; FEATFLOW; Finite Elements; First discretise then optimise; First discretize then optimize; First optimise then discretise; First optimize then discretize; Flow-Around-Cylinder; Full Newton-SAND; Heat equation; Hierarchical; Hierarchical solution concept; Inexact Newton; Inverse Problems; KKT system; Large-Scale; linear complexity; Monolithic; Multigrid; Multigrid-Krylov; Multilevel; Nonparametric finite elements; Nonstationary; OPTFLOW; Optimisation; Optimization; PDE Constraints; saddle point; SAND; Schur complement preconditioning; Space-time; SQP; Theta schema; Theta scheme; Time-dependent; Transient; Unstructured Grids; 510

Record Details Similar Records Cite « Share

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Köster, M. (2011). A Hierarchical Flow Solver for Optimisation with PDE Constraints. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-6950

Chicago Manual of Style (16^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Doctoral Dissertation, Technische Universität Dortmund. Accessed March 06, 2021. http://dx.doi.org/10.17877/DE290R-6950.

MLA Handbook (7^th Edition):

Köster, Michael. “A Hierarchical Flow Solver for Optimisation with PDE Constraints.” 2011. Web. 06 Mar 2021.

Vancouver:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2011. [cited 2021 Mar 06]. Available from: http://dx.doi.org/10.17877/DE290R-6950.

Council of Science Editors:

Köster M. A Hierarchical Flow Solver for Optimisation with PDE Constraints. [Doctoral Dissertation]. Technische Universität Dortmund; 2011. Available from: http://dx.doi.org/10.17877/DE290R-6950

		in
And / Or
		in
And / Or
		in
And / Or
		in

Open Access Theses and Dissertations