A second-order method for Poisson's equation with discontinuous<br/><br/>coefficients and singular sources

Wednesday, March 25, 2009 - 3:15pm - 4:00pm
EE/CS 3-180
Joseph Teran (University of California, Los Angeles)
Numerical simulation of moving interface problems often requires the
solution of elliptic PDEs involving coefficients that can be
discontinuous and sources that are singular. Since the interface is
moving, it is advantageous to solve the problem on a fixed Eulerian
grid which does not conform to the interface as it moves. We propose
an intuitive new method which acheives second order accurate results
in L-infinity on a fixed cartesian grid with embedded interfaces. The
method is largely independent of the geometry and the interface can be
represented either as an arbitrary (closed) segmented curve or a
levelset. The problem is formulated as a variational constrained
minimization problem which preserves a symmetric positive definite
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