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Rapid Evaluation of Multiple Integrals Over All Cells in a Mesh

IP.com Disclosure Number: IPCOM000043408D
Original Publication Date: 1984-Aug-01
Included in the Prior Art Database: 2005-Feb-04

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Weeks, WT Young, HW [+details]


A significant reduction is achieved in the time required for the computer evaluation of multiple integrals over all circuit cells in a mesh of cells by the use of an algorithm for performing multiple integrals at the grid (mesh) vertices of all the cells being considered. Let x1, x2, ..., xn be a system of n orthogonal curvilinear coordinates, and consider the mesh of cells generated by the constant coordinate surfaces. xk = ak (ik) = constant wherek = 1, 2, ..., n and ik = 0, 1, ..., Nk . Suppose it is required to evaluate the integral (Image Omitted) for every cell in the mesh, as is often the case in the numerical solution of integral equations or in the application of the finite element method. If a function f(x1,x2,...,xn) can be found such that which is a well-known result.