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Numerical grid generator based on Moser’s deformation method. (English) Zbl 0801.65115
Adaptive grid generators are strongly needed for the solution of different practical problems. In this context an important result asserts that: If a transformation from a subset \(D\) of \(\mathbb{R}^ 3\) to a cube \(B\) in \(\mathbb{R}^ 2\) is harmonic and maps the boundary of \(K\) onto the boundary of \(B\) in a 1-1 way, its Jacobian never vanishes.
Jacobian vanishing is the leading cause of grid folding, and the deformation method, inspired by a result from Moser, provides conditions to avoid this. The deformation method of grid generation is a grid generator which controls the cell size directly and precisely. Each node is moved to a new position, according to a system of ordinary differential equations. Some calculations (method implementation) are exhibitted.

MSC:
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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