sfepy.discrete.simplex_cubature module¶
Generate simplex quadrature points. Code taken and adapted from pytools/hedge by Andreas Kloeckner.
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sfepy.discrete.simplex_cubature.
generate_decreasing_nonnegative_tuples_summing_to
(n, length, min=0, max=None)[source]¶
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sfepy.discrete.simplex_cubature.
generate_permutations
(original)[source]¶ Generate all permutations of the list `original’.
Nicked from http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/252178
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sfepy.discrete.simplex_cubature.
generate_unique_permutations
(original)[source]¶ Generate all unique permutations of the list `original’.
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sfepy.discrete.simplex_cubature.
get_simplex_cubature
(order, dimension)[source]¶ Cubature on an M{n}-simplex.
cf. A. Grundmann and H.M. Moeller, Invariant integration formulas for the n-simplex by combinatorial methods, SIAM J. Numer. Anal. 15 (1978), 282–290.
This cubature rule has both negative and positive weights. It is exact for polynomials up to order 2s+1, where s is given as order. The integration domain is the unit simplex
T_n := \{(x_1, \dots, x_n): x_i \ge -1, \sum_i x_i \le -1\}