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The superior convergence properties of orthogonal polynomials are exploited along the direction of symmetry of a translatory symmetric model part. In the perpendicular directions and in the remaining model parts, standard finite elements are applied. The examples indicate a substantial saving of computational resources for both the 2D and 3D case.
In model parts which are geometrically symmetric but in which an unsymmetric field distribution is expected, a hybrid method based on a tensor-product grid of finite elements and orthogonal polynomials is applied. The finite elements ensure a flexible approximation of all geometrical details whereas the orthogonal polynomials applied along the direction of symmetry offer a superlinear convergence...
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