Splitting Extrapolation Method For Solving Second Order Partial Differential Equations With Curved Boundary By Using Domain Decomposition And Double-quadratic Isoparametric Finite Element

Finite element splitting extrapolation based on domain decomposition and double-quadratic isoparametric trasformation is a new effective technique for solving large scale scientific and engineering problems with curved boundary. By means of double-quadratic isoparametric trasformation, we can convert a problem with curved boundary to a problem on polyhedron. By means of domain decomposition , a large scale multidimensional problem is turned into several smaller discrete subproblems , which can reduce computing scale greatly. If we can get, a multiparameter asymptotic expansion of double-quadratic isoparametric finite element errors on coarse grid with respect to independent grid setps , we can get several splitting extrapolation formulas.Thercfore after solving those smaller discrete subproblems with similar sizes on coarse grid in parallcl,wc can get a global fine grid approximation with higher accuracy for that large scale multidimensional problem only by the formulas of the splitting extrapolation method. Therefore the method can improve accuracy, make full use of parallel computers and reduce computering scale greatly.What's more, the algorithm is also effective to solve partial differential equations with discontinuous coefficients...