Results 231 to 240 of about 3,365,148 (277)

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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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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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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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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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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Boundary Integral Equations

1983
This chapter is concerned with the introduction of the basic integral equations for two-dimensional elastic linear material problems. It starts by briefly reviewing the partial differential equations for linear elastic material and introducing the necessary notations involved in the formulation.
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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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Boundary Integral Equations

1991
This article is devoted to boundary integral equations and their application to the solution of boundary and initial-boundary value problems for partial differential equations.
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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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Boundary Integral Equations for the Three-Dimensional Helmholtz Equation

SIAM Review, 1974
The relation between various boundary integral equation formulations of Dirichlet and Neumann problems for the three-dimensional Helmholtz equation is clarified. The integral equations derived using single or double layer distributions as well as those based on the Helmholtz representation using an unmodified free space Green’s function are presented ...
Kleinman, R. E., Roach, G. F.
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