A multiresolution method of moments for triangular meshes

Vipiana, F.; Pirinoli, Paola; Vecchi, G.

doi:10.1109/tap.2005.850710

Cited by 88 publications

(67 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It became extremely important to develop techniques that would improve conditioning of the linear system. In the 21st century research on various regularization and preconditioning techniques [42][43][44][45][46][47] as well as on novel integral equation formulations [48][49][50][51][52] and discretization techniques [53][54][55][56][57][58][59][60] has been very active. The research on these areas is still ongoing [61].…”

Section: Historical Overviewmentioning

confidence: 99%

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

View full text Add to dashboard Cite

Abstract-During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.

show abstract

Section: Historical Overviewmentioning

confidence: 99%

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

Ylä‐Oijala¹,

Markkanen²,

Järvenpää³

et al. 2014

PIER

View full text Add to dashboard Cite

show abstract

“…To this end, one has to find a set of completely curl-free basis functions. Few research work has devoted to it [22]. Thus, it is formidable to find a completely curl-free basis in the RWG space.…”

Section: Divergence-free Field Removalmentioning

confidence: 99%

A Novel Fast Solver for Poisson's Equation With Neumann Boundary Condition

Ma¹,

Chew²,

Jiang³

2013

PIER

View full text Add to dashboard Cite

Abstract-In this paper, we present a novel fast method to solve Poisson's equation in an arbitrary two dimensional region with Neumann boundary condition, which are frequently encountered in solving electrostatic boundary problems. The basic idea is to solve the original Poisson's equation by a two-step procedure. In the first stage, we expand the electric field of interest by a set of tree basis functions and solve it with a fast tree solver in O(N ) operations. The field such obtained, however, fails to expand the exact field because the tree basis is not curl-free. Despite of this, we can retrieve the correct electric field by purging the divergence-free field. Next, for the second stage, we find the potential distribution rapidly with a same fast solution of O(N ) complexity. As a result, the proposed method dramatically reduces solution time compared with traditional FEM methods. In addition, it is the first time that the loop-tree decomposition technique has been introduced to develop fast Poisson solvers. Numerical examples including electrostatic simulations are presented to demonstrate the efficiency of the proposed method.

show abstract

“…The basic idea in building the gRWG functions is to extend to non-simplex cells the generation process for multi-level RWG functions, described in [11,16,17] for the case of a hierarchic mesh (that has only triangular cells).…”

Section: Generalized Rwgmentioning

confidence: 99%

Two-tier non-simplex grid hierarchic basis for general 3D meshes

Vipiana

Andriulli

Vecchi

2009

Waves in Random and Complex Media

View full text Add to dashboard Cite

This paper deals with hierarchical bases for the preconditioning of the Electric Field Integral Equation on arbitrary 3D meshes with triangular cells. The basis functions are constructed on subsequent groupings of the initial triangular cells, which give rise to a nested family of meshes with non-simplex cells. The previously published hierarchic set of basis functions acts as a preconditioner for dense meshes, but it may lose effectiveness when the domain of the most extended basis functions is comparable with the wavelength, thus limiting the application range of the method. The present work undertakes to overcome this limitation by introducing two tiers of basis functions, related to the hierarchic cell groupings. By suitably modifying the grouping algorithm a coarser level is obtained, on which non-hierarchic basis functions are defined. Hierarchy in the basis function defined on detail meshes is preserved instead. Numerical results show the effectiveness for structures with electrical sizes beyond the resonance region.

show abstract

A multiresolution method of moments for triangular meshes

Cited by 88 publications

References 20 publications

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

SURFACE AND VOLUME INTEGRAL EQUATION METHODS FOR TIME-HARMONIC SOLUTIONS OF MAXWELL'S EQUATIONS (Invited Paper)

A Novel Fast Solver for Poisson's Equation With Neumann Boundary Condition

Two-tier non-simplex grid hierarchic basis for general 3D meshes

Contact Info

Product

Resources

About