subject:(Helmholtz problem)

University of Delaware

1. Kapita, Shelvean. Plane wave discontinuous Galerkin methods for acoustic scattering.

Degree: PhD, University of Delaware, Department of Mathematical Sciences, 2016, University of Delaware

URL: http://udspace.udel.edu/handle/19716/19983

► We apply the Plane Wave Discontinuous Galerkin (PWDG) method to study the direct scattering of acoustic waves from impenetrable obstacles. In the first part of… (more)

Subjects/Keywords: Galerkin methods.; Sound-waves – Scattering.; Helmholtz equation.; Dirichlet problem.; Neumann problem.

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APA (6^th Edition):

Kapita, S. (2016). Plane wave discontinuous Galerkin methods for acoustic scattering. (Doctoral Dissertation). University of Delaware. Retrieved from http://udspace.udel.edu/handle/19716/19983

Chicago Manual of Style (16^th Edition):

Kapita, Shelvean. “Plane wave discontinuous Galerkin methods for acoustic scattering.” 2016. Doctoral Dissertation, University of Delaware. Accessed April 15, 2021. http://udspace.udel.edu/handle/19716/19983.

MLA Handbook (7^th Edition):

Kapita, Shelvean. “Plane wave discontinuous Galerkin methods for acoustic scattering.” 2016. Web. 15 Apr 2021.

Vancouver:

Kapita S. Plane wave discontinuous Galerkin methods for acoustic scattering. [Internet] [Doctoral dissertation]. University of Delaware; 2016. [cited 2021 Apr 15]. Available from: http://udspace.udel.edu/handle/19716/19983.

Council of Science Editors:

Kapita S. Plane wave discontinuous Galerkin methods for acoustic scattering. [Doctoral Dissertation]. University of Delaware; 2016. Available from: http://udspace.udel.edu/handle/19716/19983

Brigham Young University

2. Acosta, Sebastian Ignacio. A Multi-Frequency Inverse Source Problem for the Helmholtz Equation.

Degree: MS, 2011, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3510&context=etd

► The inverse source problem for the Helmholtz equation is studied. An unknown source is to be identified from the knowledge of its radiated wave. The… (more)

Subjects/Keywords: Inverse source problem; Helmholtz equation; multi-frequency; Mathematics

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APA (6^th Edition):

Acosta, S. I. (2011). A Multi-Frequency Inverse Source Problem for the Helmholtz Equation. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3510&context=etd

Chicago Manual of Style (16^th Edition):

Acosta, Sebastian Ignacio. “A Multi-Frequency Inverse Source Problem for the Helmholtz Equation.” 2011. Masters Thesis, Brigham Young University. Accessed April 15, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3510&context=etd.

MLA Handbook (7^th Edition):

Acosta, Sebastian Ignacio. “A Multi-Frequency Inverse Source Problem for the Helmholtz Equation.” 2011. Web. 15 Apr 2021.

Vancouver:

Acosta SI. A Multi-Frequency Inverse Source Problem for the Helmholtz Equation. [Internet] [Masters thesis]. Brigham Young University; 2011. [cited 2021 Apr 15]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3510&context=etd.

Council of Science Editors:

Acosta SI. A Multi-Frequency Inverse Source Problem for the Helmholtz Equation. [Masters Thesis]. Brigham Young University; 2011. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=3510&context=etd

New Jersey Institute of Technology

3. Qi, Haiyang. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.

Degree: PhD, Mathematical Sciences, 2017, New Jersey Institute of Technology

URL: https://digitalcommons.njit.edu/dissertations/38

► In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite… (more)

▼ In this dissertation, an in-depth comparison between boundary integral equation solvers and Domain Decomposition Methods (DDM) for frequency domain Helmholtz transmission problems in composite two-dimensional media is presented. Composite media are characterized by piece-wise constant material properties (i.e., index of refraction) and thus, they exhibit interfaces of material discontinuity and multiple junctions. Whenever possible to use, boundary integral methods for solution of Helmholtz boundary value problems are computationally advantageous. Indeed, in addition to the dimensional reduction and straightforward enforcement of the radiation conditions that these methods enjoy, they do not suffer from the pollution effect present in volumetric discretization. The reformulation of Helmholtz transmission problems in composite media in terms of boundary integral equations via multi-traces constitutes one of the recent success stories in the boundary integral equation community. Multi-trace formulations (MTF) incorporate local Dirichlet and Neumann traces on subdomains within Green’s identities and use restriction and extension by zero operators to enforce the intradomain continuity of the fields and fluxes. Through usage of subdomain Calderon projectors, the transmission problem is cast into a linear system form whose unknowns are local Dirichlet and Neumann traces (two such traces per interface of material discontinuity) and whose operator matrix consists of diagonal block boundary integral operators associated with the subdomains and extension/projections off diagonal blocks. This particular form of the matrix operator associated with MTF is amenable to operator preconditioning via Calderon projectors. DDM rely on subdomain solutions that are matched via transmission conditions on the subdomain interfaces that are equivalent to the physical continuity of fields and traces. By choosing the appropriate transmission conditions, the convergence of DDM for frequency domain scattering problems can be accelerated. Traditionally, the intradomain transmission conditions were chosen to be the classical outgoing Robin/impedance boundary conditions. When the ensuing DDM linear system is solved via Krylov subspace methods, the convergence of DDM with classical Robin transmission conditions is slow and adversely affected by the number of subdomains. Heuristically, this behavior is explained by the fact that Robin boundary conditions are first order approximations of transparent boundary conditions, and thus there is significant information that is reflected back into a given subdomain from adjacent subdomains. Clearly, using more sophisticated transparent boundary conditions facilitates the information exchange between subdomains. For instance, Dirichlet-to-Neumann (DtN) operators of adjacent domains or suitable approximations of these can be used in the form of generalized Robin boundary conditions to increase the rate of the convergence of iterative solvers of DDM linear systems.… Advisors/Committee Members: Catalin C. Turc, Michael Siegel, Eliza Zoi-Heleni Michalopoulou.

Subjects/Keywords: Helmholtz transmission problem; Boundary integral equation; Domain decomposition method; Mathematics

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APA (6^th Edition):

Qi, H. (2017). Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/38

Chicago Manual of Style (16^th Edition):

Qi, Haiyang. “Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.” 2017. Doctoral Dissertation, New Jersey Institute of Technology. Accessed April 15, 2021. https://digitalcommons.njit.edu/dissertations/38.

MLA Handbook (7^th Edition):

Qi, Haiyang. “Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters.” 2017. Web. 15 Apr 2021.

Vancouver:

Qi H. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2017. [cited 2021 Apr 15]. Available from: https://digitalcommons.njit.edu/dissertations/38.

Council of Science Editors:

Qi H. Boundary integral equation based numerical solutions of helmholtz transmission problems for composite scatters. [Doctoral Dissertation]. New Jersey Institute of Technology; 2017. Available from: https://digitalcommons.njit.edu/dissertations/38

4. Amad, Alan Alves Santana. Recuperação de aproximações de alta ordem para o problema de Helmholtz.

Degree: 2012, Laboratório Nacional de Computação Científica; Programa de Pós-Graduação de Modelagem Computacional; LNCC; Brasil; Coordenação de Pós-Graduação e Aperfeiçoamento

URL: https://tede.lncc.br/handle/tede/272

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes)

Numerical methods to solve the Helmholtz equation have to deal with the so-called numerical pollution effect generated by the phase error in the approximation solution. The Quasi Optimal Petrov-Galerkin method (QOPG) proposed by Loula and Fernandes (2009) and the Quasi Optimal Finite Difference method (QOFD) proposed by Fernandes and Loula (2010) present optimal rates of convergence and reduced pollution effects when applied to Helmholtz problems with large wave numbers. Both QOPG and QOFD stencils are obtained numerically by minimizing a least squares functional of the local truncation error for plane wave solutions at any direction. In one dimension this formulations leads to a nodally exact stencil, with no truncation error, for uniform or non-uniform meshes. In two dimensions, when applied to a uniform cartesian grid, a 9-point sixth order stencil is derived with the same truncation error of the Quasi Stabilized Finite Element Method (QSFEM) introduced by Babu\v ska et al. (1995). In the present work a post-processing method is proposed to recover higher-order approximations based on QOPG/QOFD formulations for Helmholtz problem on nested meshes. This approach is interesting because the pollution effects are reduced by QOPG/QOFD formulations and highly accurate approximations are obtained by the proposed post-processing technique with low computational cost. It is also presented a technique for exactly impose Robin boundary conditions in order to preserve the sixth order of the truncation error in incomplete stencils of QOFD at the boundary. We presented numerical simulations, of the results obtained for the proposed post-processing using Dirichlet and Robin boundary conditions for the formulations QOPG/QOFD.

Os métodos numéricos para resolver a equação de Helmholtz têm de lidar com o assim chamado efeito de poluição numérica, gerado pelo erro de fase na solução aproximada. Para reduzir o efeito de poluição do problema de Helmholtz, foram desenvolvidos métodos de poluição mínima, tais como o método Quasi Optimal Petrov-Galerkin (QOPG), proposto por Loula e Fernandes (2009), e o método Quasi Optimal Finite Difference (QOFD) proposto por Fernandes e Loula (2010). Os stencils do QOFD e do QOPG são obtidos numericamente pela minimização do funcional de mínimos quadrados do erro de truncamento local para soluções de ondas planas em…

Advisors/Committee Members: Loula, Abimael Fernando Dourado, Loula, Abimael Fernando Dourado, Fernandes, Daniel Thomes, Carmo, Eduardo Gomes Dutra do, Malta, Sandra Mara Cardoso, Almeida, Regina Célia Cerqueira de.

Subjects/Keywords: Problema de Helmholtz; Pós-processamento; Poluição numérica; Helmholtz problem; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

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

APA (6^th Edition):

Amad, A. A. S. (2012). Recuperação de aproximações de alta ordem para o problema de Helmholtz. (Masters Thesis). Laboratório Nacional de Computação Científica; Programa de Pós-Graduação de Modelagem Computacional; LNCC; Brasil; Coordenação de Pós-Graduação e Aperfeiçoamento. Retrieved from https://tede.lncc.br/handle/tede/272

Chicago Manual of Style (16^th Edition):

Amad, Alan Alves Santana. “Recuperação de aproximações de alta ordem para o problema de Helmholtz.” 2012. Masters Thesis, Laboratório Nacional de Computação Científica; Programa de Pós-Graduação de Modelagem Computacional; LNCC; Brasil; Coordenação de Pós-Graduação e Aperfeiçoamento. Accessed April 15, 2021. https://tede.lncc.br/handle/tede/272.

MLA Handbook (7^th Edition):

Amad, Alan Alves Santana. “Recuperação de aproximações de alta ordem para o problema de Helmholtz.” 2012. Web. 15 Apr 2021.

Vancouver:

Amad AAS. Recuperação de aproximações de alta ordem para o problema de Helmholtz. [Internet] [Masters thesis]. Laboratório Nacional de Computação Científica; Programa de Pós-Graduação de Modelagem Computacional; LNCC; Brasil; Coordenação de Pós-Graduação e Aperfeiçoamento; 2012. [cited 2021 Apr 15]. Available from: https://tede.lncc.br/handle/tede/272.

Council of Science Editors:

Amad AAS. Recuperação de aproximações de alta ordem para o problema de Helmholtz. [Masters Thesis]. Laboratório Nacional de Computação Científica; Programa de Pós-Graduação de Modelagem Computacional; LNCC; Brasil; Coordenação de Pós-Graduação e Aperfeiçoamento; 2012. Available from: https://tede.lncc.br/handle/tede/272

NSYSU

5. Yan, Kang-Ming. Super-geometric Convergence of Trefftz Method for Helmholtz Equation.

Degree: Master, Applied Mathematics, 2012, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0807112-112527

► In literature Trefftz method normally has geometric (exponential) convergence. Recently many scholars have found that spectral method in some cases can converge faster than exponential,… (more)

Subjects/Keywords: super-geometric convergence; rate of convergence; singularity analysis; Trefftz method; Helmholtz equation; boundary value problem

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APA (6^th Edition):

Yan, K. (2012). Super-geometric Convergence of Trefftz Method for Helmholtz Equation. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0807112-112527

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):

Yan, Kang-Ming. “Super-geometric Convergence of Trefftz Method for Helmholtz Equation.” 2012. Thesis, NSYSU. Accessed April 15, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0807112-112527.

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

MLA Handbook (7^th Edition):

Yan, Kang-Ming. “Super-geometric Convergence of Trefftz Method for Helmholtz Equation.” 2012. Web. 15 Apr 2021.

Vancouver:

Yan K. Super-geometric Convergence of Trefftz Method for Helmholtz Equation. [Internet] [Thesis]. NSYSU; 2012. [cited 2021 Apr 15]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0807112-112527.

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

Council of Science Editors:

Yan K. Super-geometric Convergence of Trefftz Method for Helmholtz Equation. [Thesis]. NSYSU; 2012. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0807112-112527

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

Delft University of Technology

6. Diao, H. (author). Fourier Analysis of Iterative Methods for the Helmholtz Problem.

Degree: 2012, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

►

This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues… (more)

Subjects/Keywords: Helmholtz problem; Krylov subspace methods; multigrid method; multilevel Krylov multigrid method; shifted Laplacian preconditioner; deflation operator; Fourier analysis

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

APA (6^th Edition):

Diao, H. (. (2012). Fourier Analysis of Iterative Methods for the Helmholtz Problem. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

Chicago Manual of Style (16^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Masters Thesis, Delft University of Technology. Accessed April 15, 2021. http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

MLA Handbook (7^th Edition):

Diao, H (author). “Fourier Analysis of Iterative Methods for the Helmholtz Problem.” 2012. Web. 15 Apr 2021.

Vancouver:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Internet] [Masters thesis]. Delft University of Technology; 2012. [cited 2021 Apr 15]. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8.

Council of Science Editors:

Diao H(. Fourier Analysis of Iterative Methods for the Helmholtz Problem. [Masters Thesis]. Delft University of Technology; 2012. Available from: http://resolver.tudelft.nl/uuid:d82de64b-b446-4df6-b335-36a3e058c8f8

7. -1218-7450. Implicit boundary integral methods.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32830

► Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary… (more)

▼ Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary integrals in a level set framework, where the boundaries are described implicitly as the zero level set of a Lipschitz function. The advantage of IBIMs is that they can work on a fixed Cartesian grid without having to parametrize the boundaries. This dissertation extends the IBIM model and develops algorithms for problems in two application areas. The first part of this dissertation considers nonlinear interface dynamics driven by bulk diffusion, which involves solving Dirichlet Laplace Problems for multiply connected regions and propagating the interface according to the solutions of the PDE at each time instant. We develop an algorithm that inherits the advantages of both level set methods (LSMs) and BIMs to simulate the nonlocal front propagation problem with possible topological changes. Simulation results in both 2D and 3D are provided to demonstrate the effectiveness of the algorithm. The second part considers wave scattering problems in unbounded domains. To obtain solutions at eigenfrequencies, boundary integral formulations use a combination of double and single layer potentials to cover the null space of the single layer integral operator. However, the double layer potential leads to a hypersingular integral in Neumann problems. Traditional schemes involve an interpretation of the integral as its Hadamard's Finite Part or a complicated process of element kernel regularization. In this thesis, we introduce an extrapolatory implicit boundary integral method (EIBIM) that evaluates the natural definition of the BIM. It is able to solve the Helmholtz problems at eigenfrequencies and requires no extra complication in different dimensions. We illustrate numerical results in both 2D and 3D for various boundary shapes, which are implicitly described by level set functions. Advisors/Committee Members: Tsai, Yen-Hsi R. (advisor), Arbogast, Todd (committee member), Biros, George (committee member), Engquist, Bjorn (committee member), Ren, Kui (committee member).

Subjects/Keywords: Boundary integral methods; Level set methods; Mullins-Sekerka; Helmholtz equation; Laplace equation; Multiply connected domain; Exterior problem; Differential equation

11 more images…

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APA (6^th Edition):

-1218-7450. (2015). Implicit boundary integral methods. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed April 15, 2021. http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Web. 15 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-1218-7450. Implicit boundary integral methods. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-1218-7450. Implicit boundary integral methods. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Vienna

8. Strempel, Mark. The reduced basis method for the Helmholtz problem.

Degree: 2020, University of Vienna

URL: http://othes.univie.ac.at/60794/

►

Ziel der Arbeit ist es die reduced basis method (RBM) numerisch zu untersuchen. Die RBM ist eine model order reduction (MOR) Methode für das lösen… (more)

▼

Ziel der Arbeit ist es die reduced basis method (RBM) numerisch zu untersuchen. Die RBM ist eine model order reduction (MOR) Methode für das lösen von parameterabhängigen Differentialgleichungen. Die RBM baut auf bestehenden Verfahren wie z.B. der finite element method (FEM) auf. Das Ziel der RBM ist es einen reduzierten reduced basis (RB) Raum auf Basis von bestehenden finite element (FE)-Lösungen, zu konstruieren. In dem ersten Teil der Arbeit werden die RBM und zwei Ansätze, den equi-logarithmic und Greedy Ansatz, für das Konstruieren von RB-Räumen vorgestellt. Anschließend wird die RBM auf unterschiedliche Beispielprobleme an- gewendet. Die Beispielprobleme bestehen aus Beispielen für parameterisierte (coercive) Poisson und (noncoercive) Helmholtz Gleichungen. Die Numerischen Tests umfassen unter anderem Konvergenztests und Tests wie der Greedy Algorithmus auf Änderungen seiner Parameter reagiert. Außerdem werden RB-Räume die mithilfe unterschiedlicher Verfahren konstruiert wurden verglichen. Die Räume wurden durch die equi-logarithmic, equi-distant, random und Greedy Ansätze kunstruiert. Abschließend wird die Anwendungen der RBM im Kontext von optimal control und parameter estimation Problemen vorgestellt. Die Anwendungsbeispiele umfassen die Bestimmung eines Materialparameters auf Basis von Messdaten und die Minimierung der Lärmemissionen einer Flugzeugturbine.

In this thesis, we discuss the numerical performance of the reduced basis method (RBM) applied to several model problems. The reduced basis method (RBM) is a model order reduction (MOR) method for solving parametrized partial differential equations (PDEs). The RBM can be used in conjunction with the finite element method (FEM). The RBM aims to reduce the dimen- sion of the finite element (FE) space by using finite element (FE) solutions as basis functions for constructing a reduced basis (RB) space. We review the RBM and its theoretical properties such as stability and error bounds. We also introduce the equi-logarithmic and greedy approaches for constructing reduced basis (RB) spaces. We apply the RBM to coercive and noncoercive parametrized model problems. The model problems are instances of the Poisson and Helmholtz equations. We report convergence and error rates of the RBM applied to the model problems. Furthermore, we compare RB spaces constructed using equi-logarithmic, equi-distant, random, and snapshots selected by the greedy algorithm. Moreover, we investigate how the greedy al- gorithm adapts to changes in parameters. Finally we consider three model problems where the RBM is applied in the context of optimal control and parameter estimation problems. Optimal control and parameter estimation problems are a natural fit for the RBM because of its improved efficiency. The examples include the estimation of a material property from measurements and the optimization of an airplane engine.

Subjects/Keywords: 31.76 Numerische Mathematik; 31.45 Partielle Differentialgleichungen; 31.80 Angewandte Mathematik; Finite Element Methoden / Helmholtz Gleichung / Reduced Basis Methode / Model Order Reduction / Numerik / Poisson Problem; Finite element methods / Helmholtz equation / Reduced basis method / Moder order reduction / Numeric / Poisson Problem

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APA (6^th Edition):

Strempel, M. (2020). The reduced basis method for the Helmholtz problem. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/60794/

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):

Strempel, Mark. “The reduced basis method for the Helmholtz problem.” 2020. Thesis, University of Vienna. Accessed April 15, 2021. http://othes.univie.ac.at/60794/.

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

MLA Handbook (7^th Edition):

Strempel, Mark. “The reduced basis method for the Helmholtz problem.” 2020. Web. 15 Apr 2021.

Vancouver:

Strempel M. The reduced basis method for the Helmholtz problem. [Internet] [Thesis]. University of Vienna; 2020. [cited 2021 Apr 15]. Available from: http://othes.univie.ac.at/60794/.

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

Council of Science Editors:

Strempel M. The reduced basis method for the Helmholtz problem. [Thesis]. University of Vienna; 2020. Available from: http://othes.univie.ac.at/60794/

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

9. Costa, José Manuel Hipólito Firmino da. Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3.

Degree: 2019, Universidade Aberta

URL: http://hdl.handle.net/10400.2/8860

► In this paper we want to generate an appropriate set of source points for the method of fun-damental solutions (MFS). The point set is intended… (more)

Subjects/Keywords: Ondas acústicas; Distribuição de pontos; Superfície estrela; Método das soluções fundamentais; Equação de Helmholtz; Interação de Coulomb; Point distribution; Star surface; Method of fundamental solutions; Helmholtz equation; External problem; Coulomb interaction; Domínio/Área Científica::Ciências Naturais::Matemáticas; ODS::04:Educação de Qualidade

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APA (6^th Edition):

Costa, J. M. H. F. d. (2019). Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3. (Masters Thesis). Universidade Aberta. Retrieved from http://hdl.handle.net/10400.2/8860

Chicago Manual of Style (16^th Edition):

Costa, José Manuel Hipólito Firmino da. “Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3.” 2019. Masters Thesis, Universidade Aberta. Accessed April 15, 2021. http://hdl.handle.net/10400.2/8860.

MLA Handbook (7^th Edition):

Costa, José Manuel Hipólito Firmino da. “Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3.” 2019. Web. 15 Apr 2021.

Vancouver:

Costa JMHFd. Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3. [Internet] [Masters thesis]. Universidade Aberta; 2019. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/10400.2/8860.

Council of Science Editors:

Costa JMHFd. Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3. [Masters Thesis]. Universidade Aberta; 2019. Available from: http://hdl.handle.net/10400.2/8860

University of Vienna

10. Pichler, Alexander. Virtual element methods for problems in acoustics and fluid dynamics.

Degree: 2019, University of Vienna

URL: http://othes.univie.ac.at/60804/

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Diese Arbeit befasst sich mit der Einführung und Analyse von Virtuellen Elemente Methoden (VEM) für Problemstellungen in Akustik und Fluiddynamik. Implizite Definitionen der Basisfunktionen und… (more)

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Diese Arbeit befasst sich mit der Einführung und Analyse von Virtuellen Elemente Methoden (VEM) für Problemstellungen in Akustik und Fluiddynamik. Implizite Definitionen der Basisfunktionen und geeignete Projektoren auf Räume von bekannten Funktionen ermöglichen den Einsatz von allgemeinen polytopalen Netzen und bieten daher im Vergleich zu Finiten Elemente Methoden mehr Freiheit bei der Konstruktion von Zerlegungen des Grundgebietes. Als Modellprobleme in Akustik und Fluiddynamik werden das Helmholtz Problem und das Problem der Vermischung von inkompressiblen Fluiden in porösen Medien betrachtet. Für das Helmholtz Problem wird eine VEM eingeführt, die zusätzlich über die Trefftz Eigenschaft verfügt, d.h. die verwendeten Basisfunktionen liegen im Kern des Helmholtz Operators. Dies gestattet, eine vorgegebene Approximationsgenauigkeit mit deutlich weniger Freiheitsgraden als mit Standardmethoden (nicht-Trefftz Methoden) zu erreichen, jedoch mit dem Nachteil einer möglicherweise sehr schlechten Konditionierung. Die Stetigkeitsbedingungen entlang der Kanten werden in einem nichtkonformen Sinn festgesetzt, was die Konstruktion eines numerischen Prozesses zur Milderung der schlechten Konditionierung erlaubt und die Methode wettbewerbsfähig macht. Theoretische und numerische Ergebnisse werden präsentiert. Das betrachtete fluiddynamische Problem kann durch eine nichtlineare Kopplung einer elliptischen Gleichung für den Druck mit einer parabolischen für die Konzentration beschrieben werden. Es werden semidiskrete und volldiskrete Formulierungen dieses Problems basierend auf einem gemischten Zugang im Kontext der virtuellen Elemente vorgestellt und analysiert. Die hergeleiteten theoretischen Resultate werden mittels numerischer Experimente überprüft.

This thesis deals with the design and analysis of virtual element methods (VEM) for problems in acoustics and fluid dynamics. By an implicit definition of the basis functions and suitable projectors onto spaces of known functions, VEM are capable of coping with general polytopal meshes and thus provide more freedom in mesh generation, in comparison to standard finite element methods. As acoustic and fluid dynamics model problems, the Helmholtz problem and the miscible displacement of incompressible fluids in porous media, respectively, are considered. For the Helmholtz problem, a VEM is introduced that additionally fulfills the Trefftz property, i.e. the employed basis functions belong to the kernel of the Helmholtz operator. This feature allows to reach a given accuracy with significantly less degrees of freedom than with standard (non-Trefftz) methods, however at the price of a possibly severe ill-conditioning. The interelement continuity constraints are imposed in a nonconforming sense, allowing the construction of a numerical process to significantly mitigate the strong ill-conditioning and thus to render the method competitive. Theoretical and numerical results are presented. The fluid dynamics model problem under consideration can be described by a nonlinear…

Subjects/Keywords: 31.76 Numerische Mathematik; 31.45 Partielle Differentialgleichungen; 31.80 Angewandte Mathematik; Virtuelle Elemente Methoden / polygonale Netze / Helmholtz Problem / Trefftz Methoden / ebene Wellen / konforme und nichtkonforme Methoden / Strömung mischbarer Flüssigkeiten / poröse Medien; virtual element methods / polygonal meshes / Helmholtz problem / Trefftz methods / plane waves / conforming and nonconforming methods / miscible fluid flow / porous media

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

APA (6^th Edition):

Pichler, A. (2019). Virtual element methods for problems in acoustics and fluid dynamics. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/60804/

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):

Pichler, Alexander. “Virtual element methods for problems in acoustics and fluid dynamics.” 2019. Thesis, University of Vienna. Accessed April 15, 2021. http://othes.univie.ac.at/60804/.

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

MLA Handbook (7^th Edition):

Pichler, Alexander. “Virtual element methods for problems in acoustics and fluid dynamics.” 2019. Web. 15 Apr 2021.

Vancouver:

Pichler A. Virtual element methods for problems in acoustics and fluid dynamics. [Internet] [Thesis]. University of Vienna; 2019. [cited 2021 Apr 15]. Available from: http://othes.univie.ac.at/60804/.

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

Council of Science Editors:

Pichler A. Virtual element methods for problems in acoustics and fluid dynamics. [Thesis]. University of Vienna; 2019. Available from: http://othes.univie.ac.at/60804/

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

11. Diong, Mouhamadou. Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet.

Degree: Docteur es, Acoustique, 2015, Aix Marseille Université

URL: http://www.theses.fr/2015AIXM4771

►

L'un des enjeux majeurs pour les systèmes d'imagerie par diffraction acoustique et micro-onde, est l'amélioration des performances obtenues au moment de la reconstruction des objets… (more)

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L'un des enjeux majeurs pour les systèmes d'imagerie par diffraction acoustique et micro-onde, est l'amélioration des performances obtenues au moment de la reconstruction des objets étudiés. Cette amélioration peut s'effectuer par la recherche d'algorithmes d'imagerie plus performants d'une part et par la recherche d'une meilleure configuration de mesures d'autre part. La première approche (recherche d'algorithmes) permet d'améliorer le processus d'extraction de l'information présente dans un échantillon de mesures donné. Néanmoins, la qualité des résultats d'imagerie reste limitée par la quantité d'information initialement disponible. La seconde approche consiste à choisir la configuration de mesures de manière à augmenter la quantité d'information disponible dans les données. Pour cette approche, il est nécessaire de quantifier la quantité d'information dans les données. En théorie de l'estimation, ceci équivaut à quantifier la performance du système. Dans cette thèse, nous utilisons la Borne de Cramer Rao comme mesure de performance, car elle permet d'analyser la performance des systèmes de mesures sans être influencé par le choix de la méthode d'inversion utilisée. Deux analyses sont proposées dans ce manuscrit. La première consiste en l'évaluation de l'influence des facteurs expérimentaux sur la performance d'inversion. Cette analyse a été effectuée pour différents objets le tout sous une hypothèse de configuration bidimensionnelle. La seconde analyse consiste à comparer les performances de l'estimateur obtenu avec l'approximation de Born aux valeurs de la borne de Cramer Rao (BCR); l'objectif étant d'illustrer d'autres applications possibles de la BCR.

Improving the performance of diffraction based imaging systems constitutes a major issue in both acoustic and electromagnetic scattering. To solve this problem, two main approaches can be explored. The first one consists in improving the inversion algorithms used in diffraction based imaging. However, while this approach generally leads to a significant improvement of the performance of the imaging system, it remains limited by the initial amount of information available within the measurements. The second one consists in improving the measurement system in order to maximize the amount of information within the experimental data. This approach does require a quantitative mean of measuring the amount of information available. In estimation problems, the {appraisal of the} performance of the system is often used for that purpose. In this Ph.D. thesis, we use the Cramer Rao bound to assess the performance of the imaging system. In fact, this quantity has the advantage of providing an assessment which is independent from the inversion algorithm used. Two main analysis are discussed in this thesis. The first analysis explores the influence on the system's performance, of several experimental conditions such as the antennas positions, the radiation pattern of the source, the properties of the background medium, etc. Two classes of objects are considered: 2D…

Advisors/Committee Members: Lasaygues, Philippe (thesis director), Roueff, Antoine (thesis director).

Subjects/Keywords: Borne de Cramer Rao; Problème inverse; Traitement statistique du signal; Analyse de performances d'estimation; Conception optimale d'expériences; Diffraction Acoustique; Diffraction Electromagnétique; Approximation de Born; Equation de Helmholtz; Cramer Rao Bound; Inverse problem; Statistical Signal Processing; Performance analysis; Optimal Design of experiments; Diffraction; Acoustic and Electromagnetic scattering; Born Approximation; Helmholtz equation

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

APA (6^th Edition):

Diong, M. (2015). Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2015AIXM4771

Chicago Manual of Style (16^th Edition):

Diong, Mouhamadou. “Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet.” 2015. Doctoral Dissertation, Aix Marseille Université. Accessed April 15, 2021. http://www.theses.fr/2015AIXM4771.

MLA Handbook (7^th Edition):

Diong, Mouhamadou. “Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet.” 2015. Web. 15 Apr 2021.

Vancouver:

Diong M. Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet. [Internet] [Doctoral dissertation]. Aix Marseille Université 2015. [cited 2021 Apr 15]. Available from: http://www.theses.fr/2015AIXM4771.

Council of Science Editors:

Diong M. Développement d'outils statistiques pour l'amélioration de dispositifs d'imagerie acoustique et micro-onde : Conception of a logical clarinet. [Doctoral Dissertation]. Aix Marseille Université 2015. Available from: http://www.theses.fr/2015AIXM4771

Universitat Politècnica de Catalunya

12. Nadukandi, Prashanth. Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems.

Degree: Departament de Resistència de Materials i Estructures a l'Enginyeria, 2011, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/109155

► Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de… (more)

▼ Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso,… Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Oñate, E. (Eugenio) (director), García Espinosa, Julio (codirector), true (authorsendemail).

Subjects/Keywords: análisis de dispersión numérica; Cálculo finito; problema de convección–difusión–reacción; ecuación deHelmholtz; problema de Stokes; métodos de elementos finitos estabilizado; método de Petrov–Galerkin con alta-resolución; Interpolación lineal de las esténcilesdel MEF y del MDF; convection–diffusion–reaction problem; Helmholtz equation; Stokesflow; stabilized finite element methods; high-resolution Petrov–Galerkin method; dispersionanalysis; 531/534

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

APA (6^th Edition):

Nadukandi, P. (2011). Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/109155

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):

Nadukandi, Prashanth. “Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems.” 2011. Thesis, Universitat Politècnica de Catalunya. Accessed April 15, 2021. http://hdl.handle.net/10803/109155.

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

MLA Handbook (7^th Edition):

Nadukandi, Prashanth. “Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems.” 2011. Web. 15 Apr 2021.

Vancouver:

Nadukandi P. Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2011. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/10803/109155.

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

Council of Science Editors:

Nadukandi P. Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems. [Thesis]. Universitat Politècnica de Catalunya; 2011. Available from: http://hdl.handle.net/10803/109155

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

13. Liu, Xiao. Structured matrix algorithms for solving Helmholtz equation.

Degree: PhD, Engineering, 2019, Rice University

URL: http://hdl.handle.net/1911/105384

► In this dissertation, novel solution algorithms are developed for large structured linear systems such as the discretized Helmholtz equation. Firstly, we develop two parallel randomized… (more)

Subjects/Keywords: Helmholtz equation; hierarchically semiseparable matrix; randomized sampling; factorization update; exterior boundary value problem; contour integration; matrix exponential

…116 4.7 Scaling curves for solving the Helmholtz problem, based on the results in Table… …a large indeﬁnite linear system. The Helmholtz problem is used extensively in seismology… …eigenvalues in the complex plane for the Helmholtz equation with impedance boundary condition. All… …the problem in Figure 5.4. . . . . . . . . . . . . . . . . . . 148 5.6 3D Scaling test… …problem sizes. . . . 150 1 Chapter 1 Introduction In this thesis, the key problem of interest…

10 more images…

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

APA (6^th Edition):

Liu, X. (2019). Structured matrix algorithms for solving Helmholtz equation. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/105384

Chicago Manual of Style (16^th Edition):

Liu, Xiao. “Structured matrix algorithms for solving Helmholtz equation.” 2019. Doctoral Dissertation, Rice University. Accessed April 15, 2021. http://hdl.handle.net/1911/105384.

MLA Handbook (7^th Edition):

Liu, Xiao. “Structured matrix algorithms for solving Helmholtz equation.” 2019. Web. 15 Apr 2021.

Vancouver:

Liu X. Structured matrix algorithms for solving Helmholtz equation. [Internet] [Doctoral dissertation]. Rice University; 2019. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1911/105384.

Council of Science Editors:

Liu X. Structured matrix algorithms for solving Helmholtz equation. [Doctoral Dissertation]. Rice University; 2019. Available from: http://hdl.handle.net/1911/105384

Université de Montréal

14. Rioux-Lavoie, Damien. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre.

Degree: 2017, Université de Montréal

URL: http://hdl.handle.net/1866/19377

Subjects/Keywords: Smoothed particle hydrodynamics (SPH); Écoulement incompressible; Méthode de projection; Théorème de décomposition de Helmholtz-Hodge; Méthode lagrangienne; Surface libre; Multiple boundary tangent (MBT); Problème d’extrusion newtonien; Incompressible flow; Projection method; Helmholtz-Hodge decomposition theorem; Lagrangian method; Free surface; Newtonian extrusion problem; Mathematics / Mathématiques (UMI : 0405)

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

APA (6^th Edition):

Rioux-Lavoie, D. (2017). Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/19377

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):

Rioux-Lavoie, Damien. “Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre.” 2017. Thesis, Université de Montréal. Accessed April 15, 2021. http://hdl.handle.net/1866/19377.

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

MLA Handbook (7^th Edition):

Rioux-Lavoie, Damien. “Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre.” 2017. Web. 15 Apr 2021.

Vancouver:

Rioux-Lavoie D. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre. [Internet] [Thesis]. Université de Montréal; 2017. [cited 2021 Apr 15]. Available from: http://hdl.handle.net/1866/19377.

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

Council of Science Editors:

Rioux-Lavoie D. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre. [Thesis]. Université de Montréal; 2017. Available from: http://hdl.handle.net/1866/19377

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

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Open Access Theses and Dissertations