G - Physics – 06 – F
Patent
G - Physics
06
F
G06F 17/10 (2006.01) G06F 7/64 (2006.01) G06F 17/13 (2006.01) G06F 17/50 (2006.01)
Patent
CA 2275086
The present invention provides a numerical analyzing method, by which equations of every element of a phenomenon represented by partial differential equations can be solved independently from each other by the direct method or the iteration method without using any collocation method such as the domain decomposition method, the finite difference method or the finite element method. A defined domain is decomposed in mesh (S1); state vectors in each element of the mesh are approximated by polynomials of finite number of terms with respect to coordinate variables (S2); and then conditions between different undetermined coefficients satisfying given govering equations are obtained. Next equations representing relationships between the undetermined coefficients of each element (element state equations) required for satisfying continuity conditions of state vectors on peripheral boundaries of every element are obtained by the least squares method to obtain a square matrix equation (S4). Further an element matrix at that time is reduced by decomposition (S5), taking the boundary conditions given on the periphery into account, and square matrix equations thus obtained are solved either by the iteration method as it is, in case where they are separated from each other, or by the direct method as a whole (S6). State vectors at arbitrary points are calculated by using calculation results obtained in this way.
Kawai Tadahiko
Macrae & Co.
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