polynomial integration on regions defined by a triangle and a conic
We present an efficient solution to the following problem, of relevance in a numerical optimization scheme: calculation of integrals of the type EQUATION for quadratic polynomials f , ? 1 , ? 2 on a plane triangle T . The naive approach would involve consideration of the many possible shapes of T ? { f ? 0} (possibly after a convenient transformation) and parameterizing its border, in order to integrate the variables separately. Our solution involves partitioning the triangle into smaller triangles on which integration is much simpler.
optimal control symbolic integration variational discretization triangular subdivision quadratic shape functions