ACA accelerated high order BEM for Maxwell problems

Rjasanow, Sergej; Weggler, Lucy

doi:10.1007/s00466-012-0731-9

Cited by 15 publications

(9 citation statements)

References 16 publications

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“…Using the numerical analysis techniques, we observed that this was a Dirichlet problem [21], [22] which could also be handled using the BEM for curved elements. Such elements can be used to avoid the assumption about the radius of the ellipse.…”

Section: Methods Imentioning

confidence: 99%

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Computational Analysis of the Capacitance by the Boundary Element Method

Semwogerere¹,

Awich²,

Nampala³

2018

IJAPM

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The boundary element method (BEM) has had an advantage of discretizing the boundary over the finite element method and the finite difference method for so long. The curved and straight elements are crucial for the discretization process. The BEM has been of fundamental importance in as far as solving a two -dimensional Laplace problem is concerned. The study aimed at using the BEM to compute the capacitance as compared to the ordinary physics methods. The BEM and its applications were reviewed in relation to curved and straight elements. The Dirac-Delta and the Green's functions were behind the use of the BEM. A model problem was tested for analysis of the BEM with curved elements in relation to the computation of the capacitance. The MATLAB programs ( . , . , 5. , . , . ,1. , 5. , 2. , and . ) and subprograms were used among others in solving the problem and also in the analysis. Findings involved the computation of the matrix terms for curved elements in relation to the cylinder curvatures. Findings also showed and compared three methods of computing the capacitance in a model problem from electrostatics. The concentric cylinder considered in this study had different shape plates where the BEM showed a fundamental advantageous stage of the BEM in calculating the capacitance for various curvature plate shapes than any other numerical method by simply increasing on the number of elements. The BEM avoids assumptions about the inner plate and treating the situation as a connected domain.The FEM and FDM [2] and [10] are less recent than the BEM in their application to the Laplace problem. The method has been developed into a robust technique for especially modeling elasticity and acoustics [9] and [10]. In this study, the method was applied to the Laplace's equation for the exterior problems involving the evaluation of the capacitance between the concentric cylinders. The term "element" was used to mean the geometry and type of approximation to a given variable. On the other hand, the term "node" was used to define the element geometry or the variables involved in the problem.In using the BEM on the interior Laplace problem, we noted that a different number of nodes is used for the variable approximations which may be linear, quadratic or otherwise. Some of these approximations

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Section: Methods Imentioning

confidence: 99%

“…The BEM simply requires the discretization of the boundary than the whole domain. It should be noted that the BEM is more recent than the other two and has several advantages over the others that include among others: Discretizing at infinity [3], and its application to solving acoustic and general engineering science problems [2].…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of the Capacitance by the Boundary Element Method

Semwogerere¹,

Awich²,

Nampala³

2018

IJAPM

View full text Add to dashboard Cite

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“…The point q was let to be the mid-point of element r. this led to the following equivalent equations: (6) where r = 1, …, n, and n is the number of nodes. The exterior formulation simply negates the RHS of equation (6).…”

Section: Introductionmentioning

confidence: 99%

“…The FEM is vital in the understanding and the use of the BEM [4]. It should be noted that the BEM is more recent than the other two and has several advantages over the others that include among others: Discretizing at infinity [5], [6], and its application to solving acoustic and general engineering science problems.…”

Section: Introductionmentioning

confidence: 99%

Application Analysis of the Curved Elements to a Two-Dimensional Laplace Problem Using the Boundary Element Method

Semwogerere¹

2015

IJAPM

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Abstract:The boundary element method (BEM) has had an advantage of discretizing the boundary over the finite element method and the finite difference method for so long. The curved and straight elements are crucial for the discretization process. In this study, the BEM has been of fundamental importance in as far as solving a two -dimensional Laplace problem is concerned.The BEM, finite element method (FEM), and the finite difference method (FDM) and their applications were reviewed, with the BEM taking advantage of the other two in relation to curved and straight elements. The Laplace equation with its boundary integral formulation was done and the BEM applied. The Dirac-Delta and the Green's functions were behind the use of the BEM. Finally, three model problems were tested for analysis of the BEM and curved elements in relation to solving the Laplace problem. The MATLAB programs and subprograms were used among others to solve the Laplace's equation in the exterior of the Ellipse, interior of a unit circle, calculating the element data for a Dirichlet type problem. The same programs were used in computing the capacitance between the concentric cylinders and eventually in the analysis.Findings showed the fundamental advantageous stage of the curved to straight elements, the suitability of the former to the latter when finding the potential and capacitance uniquely using the BEM. However the method is not applicable to partial differential equations (PDEs) whose fundamental solutions cannot be expressed in the explicit form.

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“…This scheme was successfully applied to the analysis of anisotropic solids using fundamental solutions based on double Fourier series. The ACA was also successfully applied to high order BEM for Maxwell problems by Rjasanow and Weggler (2013) and to the meshless method MFS for potential problems. More recently, Fu and Popov (2015) modified the ACA to account for the dynamic modelling of multiple bubbles.…”

Section: Introductionmentioning

confidence: 99%

Multi-Scale Failure Analysis of Laminated Composites Using the Boundary Element Method

Rodríguez¹

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ACA accelerated high order BEM for Maxwell problems

Cited by 15 publications

References 16 publications

Computational Analysis of the Capacitance by the Boundary Element Method

Computational Analysis of the Capacitance by the Boundary Element Method

Application Analysis of the Curved Elements to a Two-Dimensional Laplace Problem Using the Boundary Element Method

Multi-Scale Failure Analysis of Laminated Composites Using the Boundary Element Method

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