Journal: Engineering Analysis with Boundary Elements

Abbreviation

Eng. Anal. Bound. Elem.

Publisher

Elsevier

Journal Volumes

ISSN

0955-7997

Description

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2003 - 200912020 - 20254
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Publications 1 - 5 of 5
  • Corrigendum to “S-PEEC-DI: Surface Partial Element Equivalent Circuit method with decoupling integrals” [Engineering Analysis with Boundary Elements 173 (2025) 106152]
    Item type: Other Journal Item
    De Lauretis, Maria; Haller, Elena; Romano, Daniele; et al. (2025)
    Engineering Analysis with Boundary Elements
  • Time-domain multiple traces boundary integral formulation for acoustic wave scattering in 2D
    Item type: Journal Article
    Jerez-Hanckes, Carlos; Labarca, Ignacio (2023)
    Engineering Analysis with Boundary Elements
    We present a novel computational scheme to solve acoustic wave transmission problems over two-dimensional composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. The continuous problem is cast as a local multiple traces time-domain boundary integral formulation. For discretization in time and space, we resort to convolution quadrature schemes coupled to a non-conforming spatial spectral discretization based on second kind Chebyshev polynomials displaying fast convergence. Computational experiments confirm convergence of multistep and multistage convolution quadrature for a variety of complex domains.
  • S-PEEC-DI: Surface Partial Element Equivalent Circuit method with decoupling integrals
    Item type: Journal Article
    De Lauretis, Maria; Haller, Elena; Romano, Daniele; et al. (2025)
    Engineering Analysis with Boundary Elements
    In computational electromagnetics, numerical methods are generally optimized for triangular or tetrahedral meshes. However, typical objects of general interest in electronics, such as diode packages or antennas, have a Manhattan-type geometry that can be modeled with orthogonal and rectangular meshes. The advantage of orthogonal meshes is that they allow analytic solutions of the integral equations. In this work, we optimize the decoupling of the integrals used in the Surface formulation of the Partial Element Equivalent Circuit (S-PEEC) method for rectangular meshes. We consider a previously proposed decoupling strategy, and we lighten the underlying math by generalizing it. The new method shows improved accuracy and computational time because the number of decoupling integrals is generally reduced. The new S-PEEC method with decoupling integrals is named S-PEEC-DI. The S-PEEC-DI method is tested on a realistic diode package and compared with the volumetric PEEC (V-PEEC) and two well-known commercial solvers.
  • On the rectangular mesh and the decomposition of a Green's-function-based quadruple integral into elementary integrals
    Item type: Journal Article
    De Lauretis, Maria; Haller, Elena; Di Murro, Francesca; et al. (2022)
    Engineering Analysis with Boundary Elements
    Computational electromagnetic problems require evaluating the electric and magnetic fields of the physical object under investigation, divided into elementary cells with a mesh. The partial element equivalent circuit (PEEC) method has recently received attention from academic and industry communities because it provides a circuit representation of the electromagnetic problem. The surface formulation, known as S-PEEC, requires computing quadruple integrals for each mesh patch. Several techniques have been developed to simplify the computational complexity of quadruple integrals but limited to triangular meshes as used in well-known methods such as the Method of Moments (MoM). However, in the S-PEEC method, the mesh can be rectangular and orthogonal, and new approaches must be investigated to simplify the quadruple integrals. This work proposes a numerical approach that treats the singularity and reduces the computational complexity of one of the two quadruple integrals used in the S-PEEC method. The accuracy and computational time are tested for representative parallel and orthogonal meshes.
  • Rapid solution of first kind boundary integral equations in $R^3$
    Item type: Journal Article
    Schmidlin, Gregor; Lage, Christian; Schwab, Christoph (2003)
    Engineering Analysis with Boundary Elements
    Weakly singular boundary integral equations $(BIEs)$ of the first kind on polyhedral surfaces $\Gamma$ in $R^3$ are discretized by Galerkin $BEM$ on shape-regular, but otherwise unstructured meshes of mesh width $h$. Strong ellipticity of the integral operator is shown to give nonsingular stiffness matrices and, for piecewise constant approximations, up to $O(h^3)$ convergence of the farfield. The condition number of the stiffness matrix behaves like $O(h^-$$^1)$ in the standard basis. An $O(N)$ agglomeration algorithm for the construction of a multilevel wavelet basis on $\Gamma$ is introduced resulting in a preconditioner which reduces the condition number to $O (|log (h)|)$. A class of kernel-independent clustering algorithms (containing the fast multipole method as special case) is introduced for approximate matrix–vector multiplication in $O(N(log(N)^3)$ memory and operations. Iterative approximate solution of the linear system by $CG$ or $GMRES$ with wavelet preconditioning and clustering-acceleration of matrix–vector multiplication is shown to yield an approximate solution in log-linear complexity which preserves the $O(h^3)$ convergence of the potentials. Numerical experiments are given which confirm the theory.
Publications 1 - 5 of 5