Wavelet-based Multigrid Methods

The multi-grid method is very useful in reducing the convergence time and error for solving systems of algebraic equations, which is obtained by discreting partial differential equations. However, when confronted with certain problems, such as problems with discontinuous or highly oscillatory coefficients problems, the standard multi-grid method is less efficient. Take this into account, this paper gives a method for solving such problems. The approach taken here is obtaining new coarse grids, interpolation and restriction operators by applying the wavelet transform to the algebraic equations which are formed by discreting partial differential equations. The paper also shows us a ILU (multilevel method) method with respect to solving the inverse of the sparse matrix. It also adopts self-adaptive technique in the algorithm. Some numerical experiments prove that the algorithm is superior to others.