2008 A QR-based fast direct solver for BEM in Dirichlet-Neumann mixed boundary value problems in two-dimensional Laplace's equation

2013 ◽  
Vol 2013.26 (0) ◽  
pp. _2008-1_-_2008-3_
Author(s):  
Hiroshi ISAKARI ◽  
Togo MINE ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO
Keyword(s):  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Two Dimensional ◽  
Laplace’S Equation ◽  
Mixed Boundary Value Problems ◽  
Laplace's Equation ◽  
Direct Solver ◽  
Fast Direct Solver

Two dimensional mixed boundary-value problems in a wedge-shaped region

1968 ◽  
Vol 64 (2) ◽  
pp. 503-505 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Integral Equation ◽  
Boundary Value Problems ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Mellin Transforms

In a recent paper Srivastav (2) considered the solution of certain two-dimensional mixed boundary-value problems in a wedge-shaped region. The problems were formulated as dual integral equations involving Mellin transforms and were reduced to the solution of a Fredholm integral equation of the second kind. In this paper it will be shown that a closed form solution to the problems treated in (2) may be obtained by elementary means.

scholarly journals Mixed Boundary-Value Problems in Potential Theory

1979 ◽  
Vol 22 (2) ◽  
pp. 91-98 ◽  
Author(s):  
A. H. England
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Mixed Boundary Conditions ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Mixed Boundary Value Problems

The problems associated with finding solutions of Laplace's equation subject to mixed boundary conditions have attracted much attention and, as a consequence, a variety of analytical techniques have been developed for the solution of such problems. Sneddon (1) has given a comprehensive account of these techniques. The object of this note is to draw attention to some simple orthogonal polynomial solutions to the most basic mixed boundary-value problems in two and threedimensional potential theory. These solutions have the advantage that most quantities of physical interest are easily evaluated in terms of known functions. Two-dimensional problems are considered in §2 and axially-symmetric three-dimensional problems in §3.

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