Sparse Surface Speed Evaluation on a Dynamic Three-Dimensional Surface Using an Iterative Partitioning Scheme
We focus on a surface evolution problem where the local surface speed depends on a computationally expensive scalar function with non-local properties. The local surface speed must be re-evaluated in each time step, even for non-moving parts of the surface, due to possibly changed properties in remote regions of the simulation domain. We present a method to evaluate the surface speed only on a sparse set of points to reduce the computational effort. This sparse set of points is generated according to application-specific requirements using an iterative partitioning scheme. We diffuse the result of a constant extrapolation in the neighborhood of the sparse points to obtain an approximation to a linear interpolation between the sparse points.
We demonstrate the method for a surface evolving with a local surface speed depending on the incident flux from a source plane above the surface. The obtained speedups range from 2 to 8 and the surface deviation is less than 3 grid-cells for all evaluated test cases.
KeywordsSurface mesh Surface evolution Interpolation Robust Scalar Sparse evaluation
The financial support by the Austrian Federal Ministry of Science, Research and Economy and the National Foundation for Research, Technology and Development is gratefully acknowledged.
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