Results 281 to 290 of about 593,564 (351)

A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation

Engineering Analysis With Boundary Elements, 2009
Mehdi Dehghan, Davoud Mirzaei
exaly   +2 more sources

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 \(\mathbb{R}^{n+1}_+\).
openaire   +2 more sources

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
openaire   +1 more source

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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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.
openaire   +2 more sources

Numerical Integration of the Boundary-Layer Equations

2000
Numerical solutions of the boundary–layer equations are based on the assumption that the differential expressions in the partial differential equations can be approximated by difference expressions. This approximation, called discretisation can be obtained from a series expansion for the velocity components in the coordinate directions.
Hermann Schlichting, Klaus Gersten
openaire   +1 more source

A Boundary Integral Equation Approach to Oxidation Modeling

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1985
Thermal oxidation of silicon involves the diffusion of oxidant molecules from the gas-oxide interface to the oxide-silicon interface, and the transport of newly formed oxide away from the latter. Under suitable formulations these two processes can be shown to be boundary-value problems of harmonic and biharmonic nature.
Thye-Lai Tung, Dimitri A. Antoniadis
openaire   +1 more source

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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Boundary Integral Equations and Boundary Elements Methods in Elastodynamics

2007
We review the application of boundary integral equation (BIE) methods to elastic wave propagation problems. BIE methods express the wavefield as an integral equation defined over the boundary of the domain studied. They can be grouped into two families.
Bouchon, Michel, Sánchez-Sesma, Francisco J.   +1 more
openaire   +2 more sources

Boundary Integral Solutions of Laplace's Equation

Bell System Technical Journal, 1978
Although Laplace's equation is simple, the region over which it is to be solved is often complicated. Both the shape of the region and the boundary conditions can induce solutions Φ which are singular at isolated points on the boundary of the region. Boundary integral equation methods are well-suited to the problem, reducing a two-dimensional partial ...
openaire   +1 more source