Numerical Analysis of Linear Wave Equations in Random Media

Christoph Schwab
ETH Zürich

For initial boundary value problems
of linear second order hyperbolic
partial differential equations whose
coefficients depend on countably
many random parameters e.g. via a
Karhunen-Loeve or a wavelet expansion,
we show analyticity of weak solutions
with respect to these parameters.
The problem is reduced to a parametric family of deterministic initial boundary value problems on an infinite dimensional parameter space.

We present convergence rates for polynomial chaos type discretizations as well as for Multi-Level Monte Carlo space-time discretizations.

Christoph Schwab,
Seminar for Applied Mathematics
ETH Zurich, CH-8092 Zurich

oint work with
Viet-Ha Hoang,
Division of Mathematical Sciences,
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371

Presentation (PDF File)

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