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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...
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided...
Optical diffraction for periodical interface belongs to relatively fewer exploited application of boundary integral equations method. Our contribution presents the formulation of diffraction problem based on vector tangential fields, for which the periodical Green function of Helmholtz equation is of key importance. There are discussed properties of obtained boundary operators with singular kernel and a numerical implementation is proposed.
We prove an a priori error estimate for the hp-version of the boundary
element method with hypersingular operators on piecewise plane open or
closed surfaces. The underlying meshes are supposed to be quasi-uniform.
The solutions of problems on polyhedral or piecewise plane open surfaces exhibit
typical singularities which limit the convergence rate of the boundary element method.
On closed surfaces, and for sufficiently smooth given data, the solution is
H1-regular whereas, on open surfaces, edge...
The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
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