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Abstract:
We will present an approach to numerical simulation on recursively
structured adaptive discretisation grids. The respective grid generation
process is based on recursive bisection of triangles along marked edges.
The resulting refinement tree is sequentialised according to a
Sierpinski space-filling curve, which leads to both minimal memory
requirements and inherently cache-efficient processing schemes. The
locality properties induced by the space-filling curve are even retained
throughout adaptive refinement of the grid. We demonstrate the
efficiency of the approach by implementing a multilevel-preconditioned
conjugate gradient solver for a simple, yet adaptive, test problem:
solving Poisson's equation on a re-entrant corner problem.
