A HIGH-DIMENSIONAL MOVING MESH STRATEGY

A moving mesh strategy for solving high dimensional PDEs is presented along the lines of the moving mesh PDE (MMPDE) approach recently devel oped in one dimension by the authors and their collaborators, With thi s strategy, a moving mesh PDE is formulated from the gradient flow equ ation for a suitable functional, and the underlying physical PDE is re placed with an extended system for computing the physical solution and the mesh. The method allows simultaneously for adaptation and mesh sk ewness controls. In certain cases the mesh function, being a harmonic map, is guaranteed to exist when the boundary of the computational dom ain is convex. Efficiency of the method is predicated upon being able to solve the moving mesh PDE in an efficient manner. Numerical results for 2D are given to demonstrate the ability of the MMPDE to concentra te mesh points and to control the mesh skewness. A spatial-eigenvalue approximate factorization scheme is used for solving the MMPDE. (C) 19 98 Elsevier Science B.V.