Results 251 to 260 of about 23,355 (280)

Preconditioning for Boundary Integral Equations

SIAM Journal on Matrix Analysis and Applications, 1992
This paper discusses three alternative preconditioning techniques to solve 3-D, mixed boundary conditions, Laplace equation problems. The direct boundary element equations are tested in conjunction with three iterative solution methods; namely, conjugate gradient on the normal equations, CGS of \textit{P. Sonneveld} [SIAM J. Sci. Stat. Comput.
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Boundary Integral Equations

2001
In Chapter 10, we examined finite element methods for the numerical solution of Laplace's equation. In this chapter, we propose an alternative approach. We introduce the idea of reformulating Laplace's equation as a boundary integral equation (BIE), and then we consider the numerical solution of Laplace's equation by numerically solving its ...
Kendall Atkinson, Weimin Han
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The Boundary Integral Equations

2019
In this chapter it is shown how differential equations are transferred into integral equations. The differential equations considered range from flow problems to elasticity. Fundamental solutions are also presented.
Gernot Beer, Benjamin Marussig, Christian Duenser   +2 more
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Sparse grids for boundary integral equations

Numerische Mathematik, 1999
The paper focuses on sparse grid discretizations for boundary integral equations applied to a 2-D unit square embedded in \(\mathbb{R}^3\). Important aspects such as approximating rates, preconditioning, aspectivity and compressions are discussed theoretically and also illustrated in some numerical tests, including piecewise constant and linear ...
Michael Griebel, Peter Oswald, Thomas Schiekofer   +2 more
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Boundary integral equation analysis on the sphere

Numerische Mathematik, 2014
This work was supported in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program Award FA9550-10-1-0180 and by the Department of Energy under contract DEFGO288ER25053. This work was supported also by the Spanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovacion) under ...
Felipe Vico, Leslie Greengard, Zydrunas Gimbutas   +2 more
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Boundary Conditions for Multidimensional Integrable Equations

Functional Analysis and Its Applications, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khabibullin, I. T., Gudkova, E. V.
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Method of Boundary Integral Equations with Hypersingular Integrals in Boundary-Value Problems

Journal of Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Parabolic Problems and Boundary Integral Equations

Mathematical Methods in the Applied Sciences, 1997
Let \(\mathbb{R}^{n+1}_+= \{(x,t): x\in\mathbb{R}^n, t\in(0,+\infty)\}\) and let \[ \partial u/\partial t-\sum^n_{i,j=1} a_{ij}(x,t)\partial^2u/\partial x_i\partial x_j+ \sum^n_{i=1} a_i(x,t)\partial u/\partial x_i+a_0(x,t)u=0\tag{\(*\)} \] be a linear, uniformly parabolic equation in \(\mathbb{R}^{n+1}_+\).
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Unified boundary integral equation and unified boundary element equation

IEEE Transactions on Magnetics, 1990
Using functional analysis, a generalized operator equation is devised to describe almost all the boundary-value problems of various physical disciplines such as electrodynamics, solid mechanics, fluid mechanics, thermodynamics, etc. From the generalized operator equation, a unique unified boundary integral equation is developed which represents almost ...
null Yuan Jiansheng, null Xie Xi, null Shao Hanguang   +2 more
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WAVELET METHODS FOR BOUNDARY INTEGRAL EQUATIONS

Communications in Numerical Methods in Engineering, 1997
The author describes a recent application of the wavelet idea to the boundary integral equation of the two-dimensional direct boundary element formulation of the Laplace equation. The results for two simple problems are also included to illustrate the expected accuracy obtained with the procedure.
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