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|The Physical Object|
In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in . A fast numerical method is presented for the simulation of complicated 3-D structures, such as inductors constructed from Litz or stranded wires, above or sandwiched between the planar lossy. Some Empirical Results on Using Multipole-Accelerated Iterative Methods to Solve 3-D Potential Integral Equations. Parallel Numerical Algorithms, () A new version of the Fast Multipole Method for the Laplace equation in three by: An algorithm is described for rapid solution of classical boundary value problems (Dirichlet an Neumann) for the Laplace equation based on iteratively solving integral equations of potential theory. CPU time requirements for previously published algorithms of this type are proportional to n 2, where n is the number of nodes in the Cited by:
A three-dimensional curvilinear hybrid finite-element–integral equation approach is developed. The hybrid finite-element–integral equation method is formulated in general curvilinear coordinates so that arbitrarily curved geometries can be modeled without approximations. The advantages of the finite-element and the integral equation methods are used to eliminate the disadvantages of both. An Efﬁcient and High-Order Accurate Boundary Integral Solver for the Stokes Equations in Three Dimensional Complex Geometries by Lexing Ying A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy Department of Computer Science New York University May Denis Zorin. In this paper a parallel iterative solver based on the Generalized Minimum Residual Method (GMRES) with complex-valued coefficients is explored, with applications to the Boundary Element Method (BEM). The solver is designed to be executed in a GPU (Graphic Processing Unit) device, exploiting its massively parallel capabilities. The BEM is a competitive method in terms of Author: Jorge Molina-Moya, Alejandro Enrique Martínez-Castro, Pablo Ortiz. Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries time, partial differential equations in rather complicated geometries have to be solved in each time step. Fig. 1 Examples for ﬂow problems in ﬁxed complicated geometries.
'This outstanding monograph represents a major milestone in the list of books on the numerical solution of integral equations deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics AbstractsCited by: T.A. Cruse: Application of the boundary integral equation method to three dimensional stress analysis, Computers and Structures, 3, , – CrossRef Google Scholar  J.C. Lachat, J.O. Watson: Effective numerical treatment of boundary integral equations: A formulation for three dimensional elastostatics, Int. J. Num. Meth. in Engng. 10 Cited by: 3. 1. Introduction. We aim to efficiently and accurately solve equations of the form (IE) a σ (x) + ∫ Ω b (x) K (x, y) c (y) σ (y) d Ω y = f (x), for all x ∈ Ω, where Ω is a domain in R 3 (either a boundary or a volume). When a ≠ 0, the integral equation is Fredholm of the second kind, which is the case for all equations presented in this work.A large class of physics problems Cited by: 9. Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, (NSF, , “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3).Cited by: