subject:(adaptive cross approximation)

INP Toulouse

1. Daquin, Priscillia. Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics.

Degree: Docteur es, Electromagnétisme et Systèmes Haute Fréquence, 2017, INP Toulouse

URL: http://www.theses.fr/2017INPT0094

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Il existe une grande quantité de méthodes numériques adaptées d’une part à la modélisation, et d'autre part à la résolution des équations de Maxwell. En… (more)

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Il existe une grande quantité de méthodes numériques adaptées d’une part à la modélisation, et d'autre part à la résolution des équations de Maxwell. En particulier, la méthode des éléments nis de frontière (BEM), ou méthode des Moments (MoM), semble appropriée pour la mise en équation des phénomènes de diffraction par des objets parfaitement conducteurs, en limitant le cadre de l'étude à la frontière entre l'objet diffractant et le milieu extérieur. Cette méthode mène systématiquement à la résolution d’un système linéaire dense, que nous parvenons à compresser en l'approchant numériquement par une matrice hiérarchique creuse, appelée H-matrice. Cette approximation peut être complétée d'une ré-agglomération permettant d'améliorer la sparsité de la H-matrice et ainsi d'optimiser davantage la résolution du système traité. La hiérarchisation du système s'effectue en considérant la matrice traitée par blocs, que l'on peut ou non compresser selon une condition d'admissibilité. L'Approximation en Croix Adaptative (ACA) ou l'Approximation en Croix Hybride (HCA) sont deux méthodes de compression que l'on peut alors appliquer aux blocs admissibles. Il existe une grande quantité de méthodes numériques adaptées d’une part à la modélisation, et d'autre part à la résolution des équations de Maxwell. En particulier, la méthode des éléments finis de frontière (BEM), ou méthode des Moments (MoM), semble appropriée pour la mise en équation des phénomènes de diffraction par des objets parfaitement conducteurs, en limitant le cadre de l'étude à la frontière entre l'objet diffractant et le milieu extérieur. Cette méthode mène systématiquement à la résolution d’un système linéaire dense, que nous parvenons à compresser en l'approchant numériquement par une matrice hiérarchique creuse, appelée H-matrice. Cette approximation peut être complétée d'une ré-agglomération permettant d'améliorer la sparsité de la H-matrice et ainsi d'optimiser davantage la résolution du système traité. La hiérarchisation du système s'effectue en considérant la matrice traitée par blocs, que l'on peut ou non compresser selon une condition d'admissibilité. L'Approximation en Croix Adaptative (ACA) ou l'Approximation en Croix Hybride (HCA) sont deux méthodes de compression que l'on peut alors appliquer aux blocs admissibles. Le travail de cette thèse consiste dans un premier temps à valider le format H-matrice en 2D et en 3D en utilisant l'ACA, puis d'y appliquer la méthode HCA, encore peu exploitée. Nous pouvons alors résoudre le système linéaire issu de la BEM en utilisant différents solveurs, directs ou non, adaptés au format hiérarchique. En particulier, nous pourrons constater l'efficacité du préconditionnement LU hiérarchique sur un solveur itératif. Nous pourrons alors appliquer ce formalisme au cas des surfaces rugueuses ou encore des fibres à cristaux photoniques (PCF). Il sera également possible de paralléliser certaines opérations sur architecture partagée afin de réduire de nouveau le coût temporel de la résolution.

A lot of numerical methods are…

Advisors/Committee Members: Poirier, Jean-René (thesis director), Perrussel, Ronan (thesis director).

Subjects/Keywords: Méthodes numériques; Equations intégrales de frontière; Matrices hiérarchiques; Adaptive Cross Approximation; Hybrid Cross Approximation; Parallélisation; Numerical methods; Boundary element method; Hierarchical matrices; Adaptive Cross Approximation; Hybrid Cross Approximation; Parallel computing

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

APA (6^th Edition):

Daquin, P. (2017). Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2017INPT0094

Chicago Manual of Style (16^th Edition):

Daquin, Priscillia. “Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics.” 2017. Doctoral Dissertation, INP Toulouse. Accessed April 18, 2021. http://www.theses.fr/2017INPT0094.

MLA Handbook (7^th Edition):

Daquin, Priscillia. “Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics.” 2017. Web. 18 Apr 2021.

Vancouver:

Daquin P. Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics. [Internet] [Doctoral dissertation]. INP Toulouse; 2017. [cited 2021 Apr 18]. Available from: http://www.theses.fr/2017INPT0094.

Council of Science Editors:

Daquin P. Méthodes quasi-optimales pour la résolution des équations intégrales de frontière en électromagnétisme : Quasi-optimal and frequency robust methods for solving integral equations in electromagnetics. [Doctoral Dissertation]. INP Toulouse; 2017. Available from: http://www.theses.fr/2017INPT0094

Stellenbosch University

2. Nel, Abraham Pieter Ben. Adaptive cross approximation for electromagnetic analysis of superconducting circuits.

Degree: MEng, Electrical and Electronic Engineering, 2019, Stellenbosch University

URL: http://hdl.handle.net/10019.1/106196

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ENGLISH ABSTRACT: Electromagnetic analysis of superconducting integrated circuits is routinely required for inductance extraction. FastHenry is a magnetoquasistatic (MQS) analysis tool suitable for this task.… (more)

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ENGLISH ABSTRACT: Electromagnetic analysis of superconducting integrated circuits is routinely required for inductance extraction. FastHenry is a magnetoquasistatic (MQS) analysis tool suitable for this task. It is based on the partial element equivalent circuit (PEEC), integral equation method, with the structure discretised into hexahedral filaments. FastHenry’s multilevel fast multipole algorithm (MLFMA) implementation is especially memory efficient, given certain approximations and algorithmic parameter choices. However, errors are introduced into the matrix representation. This thesis describes the implementation of a multilevel adaptive cross approximation solver with singular value decomposition recompression (MLACA-SVD) inside FastHenry as an alternative to its existing MLFMA solver. The thesis also presents two modified grouping strategies to further improve MLACA-SVD efficiency by compressing interactions between larger groups, while maintaining scaling performance consistent with a valid admissibility condition. MLACA-SVD compresses off-diagonal matrix blocks to a specified error tolerance, based on evaluating selected entries. Quadrature recipes presented in this thesis provide guaranteed accuracy of matrix entry evaluation. Numerical results for examples of practical interest show that the MLACA-SVD memory scaling versus number of filaments, denoted b, is practically identical to that of FastHenry’s MLFMA, and is close to O(b log b). The MLACA-SVD requires less memory for the same solution accuracy, and furthermore offers complete control over matrix approximation errors. For the examples considered, it is found to be a more efficient solver. The results of the group merging strategies show that required memory is further reduced by approximately 30%. The MLACA-SVD solver with merging requires about four times less memory than FastHenry’s MLFMA, for similar accuracy.

AFRIKAANSE OPSOMMING: Elektromagnetiese analise van supergeleidende geïntegreerde stroombane word gereeld benodig vir induktansie onttrekking. FastHenry is ’n magnetetoquastistiese (MQS) analisehulpmiddel, geskik vir hierdie taak. Dit is gebaseer op die gedeeltelike element ekwivalente stroombaan (GEES), integrale vergelykings metode, met die struktuur gediskretiseer in hexahedrale filamente. Die multivlak vinnige multipool algoritme (MVVMA) implementering in FastHenry is veral doeltreffend ten opsigte van geheue, gegewe sekere benaderings en algoritmiese parameter keuses. Foute word egter in die matriksvoorstelling ingevoer. Hierdie tesis beskryf die implementering van ’n multivlak aanpassingsvaardige kruisbenadering oplosser met enkelvoudige waarde-ontbinding herkompressie (AKO-EWOH) binne FastHenry as ’n alternatief vir die bestaande MVVMA oplosser. Die tesis bied ook twee aangepaste groeperingstrategieë aan om AKO-EWOH se doeltreffendheid verder te verbeter deur interaksies tussen groter groepe te kompres, terwyl die skaleringsuitset in ooreenstemming bly met ’n geldige toelaatbaarheidstoestand.…

Advisors/Committee Members: Botha, M. Matthys, Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering..

Subjects/Keywords: Adaptive Cross Approximation; Electromagnetic waves – Analysis; Superconducting; Integrated circuits; UCTD; UCTD

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

APA (6^th Edition):

Nel, A. P. B. (2019). Adaptive cross approximation for electromagnetic analysis of superconducting circuits. (Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/106196

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):

Nel, Abraham Pieter Ben. “Adaptive cross approximation for electromagnetic analysis of superconducting circuits.” 2019. Thesis, Stellenbosch University. Accessed April 18, 2021. http://hdl.handle.net/10019.1/106196.

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

MLA Handbook (7^th Edition):

Nel, Abraham Pieter Ben. “Adaptive cross approximation for electromagnetic analysis of superconducting circuits.” 2019. Web. 18 Apr 2021.

Vancouver:

Nel APB. Adaptive cross approximation for electromagnetic analysis of superconducting circuits. [Internet] [Thesis]. Stellenbosch University; 2019. [cited 2021 Apr 18]. Available from: http://hdl.handle.net/10019.1/106196.

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

Council of Science Editors:

Nel APB. Adaptive cross approximation for electromagnetic analysis of superconducting circuits. [Thesis]. Stellenbosch University; 2019. Available from: http://hdl.handle.net/10019.1/106196

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

University of Cincinnati

3. Bapat, Milind S. New Developments in Fast Boundary Element Method.

Degree: PhD, Engineering and Applied Science: Mechanical Engineering, 2012, University of Cincinnati

URL: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947

► Boundary element method (BEM) is a numerical technique based on integral equations. BEM has found to be very efficient for boundary value problems where… (more)

▼ Boundary element method (BEM) is a numerical technique based on integral equations. BEM has found to be very efficient for boundary value problems where the domains are infinite or singularities are involved. As a result, the use of BEM has become very popular in areas like acoustics and fracture mechanics. The standard formulation for BEM involves solution to a linear system of equations Ax=b where A is a dense and nonsymmetrical matrix. The computational time is seen to be order O(N²) with iterative solvers. The Fast multipole method (FMM) and Adaptive cross approximation (ACA) methods are two methods that have been developed in recent years to reduce the order of computation to O(N). In this research we investigate the ACA and FMM, and conduct a comparison study between the two. This research discusses the FMM in details. The FMM is a tree based algorithm to do fast matrix vector multiplication. Over the years, a variety of techniques have been developed to make FMM more efficient. Some of these techniques are studied and implemented. The research considers three different types of problems, viz. potential, acoustic and elastostatic problems for the purpose of comparison. A new L2 modification has been introduced in this research. An efficient usage of adaptive tree is also presented. Finally, a composite technique encompassing the existing strategies with the new proposed modifications has been presented as the new adaptive algorithm. An implementation of this technique, coded in FORTRAN, has yielded the capacity of solving very large engineering problems (up to 1 million DOFs) on a desktop PC in small amount of time. Numerical results have been presented which emphasize the efficiency of this new implementation. The second part of this research is to study ACA and compare with FMM. A study of ACA has been done and a modified implementation of the ACA has been proposed. This implementation has enabled one to solve a few large problems (more than a half million DOFs) on a desktop PC. Finally a comparison study has been conducted between the FMM and ACA for simple acoustic problems. It was found that the ACA is much more efficient for solving small to medium sized problems (up to 200,000 DOFs) while the FMM was found to be more efficient for large sized problems (more than 200,000 DOFs). This thesis research has significantly improved the computational efficiencies of both the FMBEM and ACA BEM towards applications of the BEM in solving real engineering problems on desktop PCs. Advisors/Committee Members: Liu, Yijun (Committee Chair).

Subjects/Keywords: Mechanical Engineering; Fast Multipole Method; Boundary Element Method; Adaptive Cross Approximation; Acoustics

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

APA (6^th Edition):

Bapat, M. S. (2012). New Developments in Fast Boundary Element Method. (Doctoral Dissertation). University of Cincinnati. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947

Chicago Manual of Style (16^th Edition):

Bapat, Milind S. “New Developments in Fast Boundary Element Method.” 2012. Doctoral Dissertation, University of Cincinnati. Accessed April 18, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947.

MLA Handbook (7^th Edition):

Bapat, Milind S. “New Developments in Fast Boundary Element Method.” 2012. Web. 18 Apr 2021.

Vancouver:

Bapat MS. New Developments in Fast Boundary Element Method. [Internet] [Doctoral dissertation]. University of Cincinnati; 2012. [cited 2021 Apr 18]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947.

Council of Science Editors:

Bapat MS. New Developments in Fast Boundary Element Method. [Doctoral Dissertation]. University of Cincinnati; 2012. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1331296947

INP Toulouse

4. Maurin, Julien. Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms.

Degree: Docteur es, Electromagnétisme et Systèmes Haute Fréquence, 2015, INP Toulouse

URL: http://www.theses.fr/2015INPT0079

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Cette étude s’inscrit dans le domaine de la simulation électromagnétique des problèmes de grande taille tels que la diffraction d’ondes planes par de larges plateformes… (more)

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Cette étude s’inscrit dans le domaine de la simulation électromagnétique des problèmes de grande taille tels que la diffraction d’ondes planes par de larges plateformes et le rayonnement d’antennes aéroportées. Elle consiste à développer une méthode combinant décomposition en sous-domaines et compression hiérarchique des équations intégrales de frontière. Pour cela, nous rappelons dans un premier temps les points importants de la méthode des équations intégrales de frontière et de leur compression hiérarchique par l’algorithme ACA (Adaptive Cross Approximation). Ensuite, nous présentons la formulation IE-DDM (Integral Equations – Domain Decomposition Method) obtenue à partir d’une représentation intégrale des sous-domaines. Les matrices résultant de la discrétisation de cette formulation sont stockées au format H-matrice (matricehiérarchique). Un solveur spécialement adapté à la résolution de la formulation IE-DDM et à sa représentation hiérarchique a été conçu. Cette étude met en évidence l’efficacité de la décomposition en sous-domaines en tant que préconditionneur des équations intégrales. De plus, la méthode développée est rapide pour la résolution des problèmes à incidences multiples ainsi que la résolution des problèmes basses fréquences

This thesis is about the electromagnetic simulation of large scale problems as the wave scattering from aircrafts and the airborne antennas radiation. It consists in the development of a method combining domain decomposition and hierarchical compression of the surface integral equations. First, we remind the principles of the boundary element method and the hierarchical representation of the surface integral equations with the Adaptive Cross Approximation algorithm. Then, we present the IE-DDM formulation obtained from a sub-domain integral representation. The matrices resulting of the discretization of the formulation are stored in the H-matrix format. A solver especially fitted with the hierarchical representation of the IE-DDM formulation has been developed. This study highlights the efficiency of the sub-domain decomposition as a preconditioner of the integral equations. Moreover, the method is fast for the resolution of multiple incidences and the resolution of low frequencies problems

Advisors/Committee Members: Barka, André (thesis director), Gobin, Vincent (thesis director).

Subjects/Keywords: Equations intégrales de surface; Décomposition en sous-domaines; Matrices hiérarchiques; Adaptive cross approximation; Factorisation LU approchée; Solveur itératif; Simulation électromagnétique; Larges plateformes; Surface integral equations; Domain decomposition; Hierarchical matrices; Adaptive cross approximation; Approximate LU factorization; Iterative solver; Computational electromagnetics; Large scale problems

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

APA (6^th Edition):

Maurin, J. (2015). Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2015INPT0079

Chicago Manual of Style (16^th Edition):

Maurin, Julien. “Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms.” 2015. Doctoral Dissertation, INP Toulouse. Accessed April 18, 2021. http://www.theses.fr/2015INPT0079.

MLA Handbook (7^th Edition):

Maurin, Julien. “Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms.” 2015. Web. 18 Apr 2021.

Vancouver:

Maurin J. Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms. [Internet] [Doctoral dissertation]. INP Toulouse; 2015. [cited 2021 Apr 18]. Available from: http://www.theses.fr/2015INPT0079.

Council of Science Editors:

Maurin J. Résolution des équations intégrales de surface par une méthode de décomposition de domaine et compression hiérarchique ACA : Application à la simulation électromagnétique des larges plateformes : Resolution of surface integral equations by a domain decomposition method and adaptive cross approximation : Application to the electromagnetic simulation of large platforms. [Doctoral Dissertation]. INP Toulouse; 2015. Available from: http://www.theses.fr/2015INPT0079

Universitat Politècnica de Catalunya

5. Tamayo Palau, José María. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.

Degree: Departament de Teoria del Senyal i Comunicacions, 2011, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/6952

► The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in… (more)

▼ The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy – machine precision – is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the… Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Rius Casals, Juan Manuel (director).

Subjects/Keywords: vertex adjacent integration; edge adjacent integration; adaptive cross approximation; impedance matrix compression; electromagnetism; numerical simulation; singular integrals; surface integral equations; fast solvers; method of moments (MOM); 517; 621.3

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

APA (6^th Edition):

Tamayo Palau, J. M. (2011). Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/6952

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):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Thesis, Universitat Politècnica de Catalunya. Accessed April 18, 2021. http://hdl.handle.net/10803/6952.

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

MLA Handbook (7^th Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Web. 18 Apr 2021.

Vancouver:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2011. [cited 2021 Apr 18]. Available from: http://hdl.handle.net/10803/6952.

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

Council of Science Editors:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Thesis]. Universitat Politècnica de Catalunya; 2011. Available from: http://hdl.handle.net/10803/6952

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

University of Lund

6. Tayli, Doruk. Computational Tools for Antenna Analysis and Design.

Degree: 2018, University of Lund

URL: https://lup.lub.lu.se/record/7d36f2c9-59a8-4fed-a8b7-c444a807f309 ; https://portal.research.lu.se/ws/files/69606844/Tayli_thesis.pdf

► Many engineers and scientists prevalently use computational tools in electromagnetics, which is also the predominant case for antennas. The ever-increasing number of applications and technologies… (more)

Subjects/Keywords: Engineering and Technology; Antenna theory; Fundamental bounds; method of moments (MoM); Characteristic modes; macro basis functions (MBFs); adaptive cross approximation (ACA); endfire arrays

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

APA (6^th Edition):

Tayli, D. (2018). Computational Tools for Antenna Analysis and Design. (Doctoral Dissertation). University of Lund. Retrieved from https://lup.lub.lu.se/record/7d36f2c9-59a8-4fed-a8b7-c444a807f309 ; https://portal.research.lu.se/ws/files/69606844/Tayli_thesis.pdf

Chicago Manual of Style (16^th Edition):

Tayli, Doruk. “Computational Tools for Antenna Analysis and Design.” 2018. Doctoral Dissertation, University of Lund. Accessed April 18, 2021. https://lup.lub.lu.se/record/7d36f2c9-59a8-4fed-a8b7-c444a807f309 ; https://portal.research.lu.se/ws/files/69606844/Tayli_thesis.pdf.

MLA Handbook (7^th Edition):

Tayli, Doruk. “Computational Tools for Antenna Analysis and Design.” 2018. Web. 18 Apr 2021.

Vancouver:

Tayli D. Computational Tools for Antenna Analysis and Design. [Internet] [Doctoral dissertation]. University of Lund; 2018. [cited 2021 Apr 18]. Available from: https://lup.lub.lu.se/record/7d36f2c9-59a8-4fed-a8b7-c444a807f309 ; https://portal.research.lu.se/ws/files/69606844/Tayli_thesis.pdf.

Council of Science Editors:

Tayli D. Computational Tools for Antenna Analysis and Design. [Doctoral Dissertation]. University of Lund; 2018. Available from: https://lup.lub.lu.se/record/7d36f2c9-59a8-4fed-a8b7-c444a807f309 ; https://portal.research.lu.se/ws/files/69606844/Tayli_thesis.pdf

7. Desiderio, Luca. H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D.

Degree: Docteur es, Mathématiques appliquées, 2017, Université Paris-Saclay (ComUE)

URL: http://www.theses.fr/2017SACLY002

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Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans… (more)

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Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans le cadre d'une collaboration avec la société Shell en vue d'optimiser la convergence des problèmes d'inversion sismique. La méthode repose sur l'utilisation des éléments finis de frontière (BEM) pour la discrétisation et sur les techniques de matrices hiérarchiques (H-matrices) pour l'accélération de la résolution du système linéaire. Dans le cadre de cette thèse on a développé un solveur direct pour les BEMs en utilisant une factorisation LU et un stockage hiérarchique. Si le concept des H-matrices est simple à comprendre, sa mise en oeuvre requiert des développements algorithmiques importants tels que la gestion de la multiplication de matrices représentées par des structures différentes (compressées ou non) qui ne comprend pas mois de 27 sous-cas. Un autre point délicat est l'utilisation des méthodes d'approximations par matrices compressées (de rang faible) dans le cadre des problèmes vectoriels. Une étude algorithmique a donc été faite pour mettre en oeuvre la méthode des H-matrices. Nous avons par ailleurs estimé théoriquement le rang faible attendu pour les noyaux oscillants, ce qui constitue une nouveauté, et montré que la méthode est utilisable en élastodynamique. En outre on a étudié l'influence des divers paramètres de la méthode en acoustique et en élastodynamique 3D, à fin de calibrer leur valeurs numériques optimales. Dans le cadre de la collaboration avec Shell, un cas test spécifique a été étudié. Il s'agit d'un problème de propagation d'une onde sismique dans un demi-espace élastique soumis à une force ponctuelle en surface. Enfin le solveur direct développé a été intégré au code COFFEE développé a POEMS (environ 25000 lignes en Fortran 90)

This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational eﬃciency. We propose a fast H-matrix based direct BEM solver.

Advisors/Committee Members: Ciarlet, Patrick (thesis director).

Subjects/Keywords: Éléments Finis de Frontière; Matrices H; Approximation adaptative croisée; Décomposition en valeurs singulières aléatoires; Élastodynamique 3D; Problèmes de vibrations forcées; Boundary element method; H-Matrix; Adaptive Cross Approximation; Randomized Singular Value Decomposition; 3D elastodynamics; Forced vibration problems; 515.6

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

APA (6^th Edition):

Desiderio, L. (2017). H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2017SACLY002

Chicago Manual of Style (16^th Edition):

Desiderio, Luca. “H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D.” 2017. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 18, 2021. http://www.theses.fr/2017SACLY002.

MLA Handbook (7^th Edition):

Desiderio, Luca. “H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D.” 2017. Web. 18 Apr 2021.

Vancouver:

Desiderio L. H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2017. [cited 2021 Apr 18]. Available from: http://www.theses.fr/2017SACLY002.

Council of Science Editors:

Desiderio L. H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations : Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2017. Available from: http://www.theses.fr/2017SACLY002

Duquesne University

8. Rogus, Brent D. The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution.

Degree: MS, Computational Mathematics, 2008, Duquesne University

URL: https://dsc.duq.edu/etd/1118

► Finding solutions to Maxwell's Equations is the key to modeling all electromagnetic phenomenon. One approach to solving Maxwell's Equations is to use an integral equation… (more)

Subjects/Keywords: adaptive cross approximation algorithm (ACA); locally corrected Nystrom method; electromagnetic scattering; body of revolution (BOR)

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

APA (6^th Edition):

Rogus, B. D. (2008). The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution. (Masters Thesis). Duquesne University. Retrieved from https://dsc.duq.edu/etd/1118

Chicago Manual of Style (16^th Edition):

Rogus, Brent D. “The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution.” 2008. Masters Thesis, Duquesne University. Accessed April 18, 2021. https://dsc.duq.edu/etd/1118.

MLA Handbook (7^th Edition):

Rogus, Brent D. “The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution.” 2008. Web. 18 Apr 2021.

Vancouver:

Rogus BD. The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution. [Internet] [Masters thesis]. Duquesne University; 2008. [cited 2021 Apr 18]. Available from: https://dsc.duq.edu/etd/1118.

Council of Science Editors:

Rogus BD. The Adaptive Cross Approximation Algorithm Applied to Electromagnetic Scattering by Bodies of Revolution. [Masters Thesis]. Duquesne University; 2008. Available from: https://dsc.duq.edu/etd/1118

9. Tibaut, Jan. Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah.

Degree: 2019, Univerza v Mariboru

URL: https://dk.um.si/IzpisGradiva.php?id=73637 ; https://dk.um.si/Dokument.php?id=139366&dn= ; https://plus.si.cobiss.net/opac7/bib/303452928?lang=sl

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V doktorski disertaciji predstavljamo hitro robno-območno integralsko metodo, ki smo jo uporabili za reševanje prenosnih pojavov v tekočini. Hitra robno-območna integralska metoda izhaja iz robno-območne… (more)

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V doktorski disertaciji predstavljamo hitro robno-območno integralsko metodo, ki smo jo uporabili za reševanje prenosnih pojavov v tekočini. Hitra robno-območna integralska metoda izhaja iz robno-območne integralske metode. Beseda hitra pove, da smo jo pospešili. Računska kompleksnost robno-območne integralske metode raste s kvadratom števila neznank. Zaradi tega hitro dosežemo zmogljivost razpoložljive računalniške opreme in smo tako omejeni na preproste primere. Z aproksimacijsko metodo zmanjšamo računsko kompleksnost robno-območne integralske metode. Uporabili smo križno aproksimacijo s hierarhično razdelitvijo matrik. Razvit algoritem smo primerjali s primeri, ki so v svetu priznani. V naših raziskavah smo rešili hitrostno-vrtinčno obliko Navier-Stokesovih enačb. Simulirali smo tok nanotekočine, ki ga žene naravna konvekcija v zaprti kotanji. Nanotekočina je zmes tekočine in delcev, ki imajo velikost nekaj nanometrov. Zapisali smo model, s katerim smo rešili tok nanotekočine, ki je vsebovala nanodelce aluminijevega oksida.

In this dissertation, we present a Fast Boundary-Domain Integral Method that was used to solve transport phenomena in fluids. The Fast Boundary-Domain Integral Method has derived from the Boundary-Domain Integral Method. The word fast states that an acceleration method was employed. The computational cost of the Boundary-Domain Integral Method increases with the square of the number of unknowns. Thus, the computational cost quickly reaches the maximal computational power. Therefore, we are limited to smaller cases. In order to reduce the computational cost of the Boundary-Domain Integral Method, an approximation procedure has to be employed. We approximated the matrices that evolve from the Boundary-Domain Integral Method with a hierarchical decomposition method and an adaptive cross approximation algorithm. The developed algorithm was tested on test cases that are recognized in the world. In this study, we solved the velocity-vorticity formulation of the Navier-Stokes equations. We simulated a buoyancy-driven flow of a nanofluid in a closed cavity. The nanofluid is a mixture of a base fluid in nanoparticles. The nanoparticles are of the size of few nanometers. We present a model to solve the flow of a nanofluid. The nanofluid contained nanoparticles of alumina.

Advisors/Committee Members: Ravnik, Jure.

Subjects/Keywords: robno-območna integralska metoda; $mathcal{H}$-struktura; križna aproksimacija; nanotekočine; prenos toplote; naravna konvekcija; hitrostno-vrtinčna oblika Navier-Stokesovih enačb; računalniška dinamika tekočin; Boundary-domain integral method; H-structure; adaptive cross approximation; nanofluids; heat transfer; natural convection; velocity-vorticity Navier-Stokes formulation; computational fluid dynamics; info:eu-repo/classification/udc/519.64:536.243(043.3)

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

APA (6^th Edition):

Tibaut, J. (2019). Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah. (Doctoral Dissertation). Univerza v Mariboru. Retrieved from https://dk.um.si/IzpisGradiva.php?id=73637 ; https://dk.um.si/Dokument.php?id=139366&dn= ; https://plus.si.cobiss.net/opac7/bib/303452928?lang=sl

Chicago Manual of Style (16^th Edition):

Tibaut, Jan. “Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah.” 2019. Doctoral Dissertation, Univerza v Mariboru. Accessed April 18, 2021. https://dk.um.si/IzpisGradiva.php?id=73637 ; https://dk.um.si/Dokument.php?id=139366&dn= ; https://plus.si.cobiss.net/opac7/bib/303452928?lang=sl.

MLA Handbook (7^th Edition):

Tibaut, Jan. “Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah.” 2019. Web. 18 Apr 2021.

Vancouver:

Tibaut J. Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah. [Internet] [Doctoral dissertation]. Univerza v Mariboru; 2019. [cited 2021 Apr 18]. Available from: https://dk.um.si/IzpisGradiva.php?id=73637 ; https://dk.um.si/Dokument.php?id=139366&dn= ; https://plus.si.cobiss.net/opac7/bib/303452928?lang=sl.

Council of Science Editors:

Tibaut J. Hitra robno-območna integralska metoda za simulacijo prenosnih pojavov v tekočinah. [Doctoral Dissertation]. Univerza v Mariboru; 2019. Available from: https://dk.um.si/IzpisGradiva.php?id=73637 ; https://dk.um.si/Dokument.php?id=139366&dn= ; https://plus.si.cobiss.net/opac7/bib/303452928?lang=sl

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