GPU accelerated computation of the isogeometric analysis stiffness matrix

A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0

“…10 In the first line we generate the knot vectors and the degrees for each component of the velocity space, with the GeoPDEs function knt_derham. This function automatically generates the knot vectors (and degrees) for the spaces in (15)- (16), and in general for any of the spline spaces of the De Rham sequence introduced in [18]. Knowing the knot vectors, we construct a scalar space for each component in the parametric domain, and then the vector-valued space of the class sp_vector, setting a div-preserving transformation.…”

“…We start with a loop over the elements in the first parametric direction, and inside the loop we use the functions msh_evaluate_col 6 An alternative assembly strategy, based on quadrature points instead of elements, was proposed in [16]. and sp_evaluate_col to compute the parametrization and the discrete basis functions in the elements of one ''column'' of the mesh, that is, fixing the element in the first parametric direction.…”

Matrix computing coprocessor for an embedded system

“…Sparse matrix vector multiplication through reordering techniques has been explored with Tesla C1060 and Tesla M2050 [1]. The computation of isogeometric analysis stiffness matrix exhibits increased speed when implemented on GeForce GTX680 [2]. However, in accelerating matrix computing, GPUs with high price and power consumption remain inefficient in embedded systems [3].…”

Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation

“…On the one hand, this has motivated the use GPU programming [9,10] for accelerating the assembly process. On the other hand, several alternatives to Gauss quadrature have been explored.…”