On numerical cubatures of singular surface integrals in boundary element methods.
On numerical solution of the Dirichlet problem by the method of locally-canonical decomposition.
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On some nonlinear potential problems.
On the boundary element method for the Signorini problem of the Laplacian.
On the Convergence of Multi-Grid Methods for a Hypersingular Integral Equation of the First Kind.
On the economical solution method for a system of linear algebraic equations.
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.
On the numerical solution of some semilinear elliptic problems.
On the Schwarz algorithms for the elliptic exterior boundary value problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...
On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical convergence...