Thursday, February 23, 9:30 am in room MTH 3206, University of Maryland,
College Park
On the Computation of Higher-Order Derivatives with the Boundary
Element Method
Prof. W. L. Wendland
Mathematisches Institut A
University of Stuttgart, Germany
wendland@mathematik.uni-stuttgart.de
In combination with the original elliptic partial differential equation
and the boundary conditions, derivatives of the generalized Green's
representation formula yield a bootstrapping algorithm for the
extraction of higher-order Cauchy data on the boundary involving singular
boundary integral operators in terms of Hadamard's finite parts.
A characterization of related commutator operators in terms of their
pseudo-homogeneous kernel expansions allows to compute arbitrarily high-order
derivatives of the solution along the boundary with the same asymptotic order
of convergence as for the desired Cauchy datum in the original boundary
integral equation provided the boundary surface is sufficiently smooth.
For polynomial surface approximation and an explicitly given fundamental
solution, the necessary kernel expansions can be computed automatically by
symbolic manipulation.
This is joint work with C. Schwab.
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