Speaker
Dr
Neeraj Sarna
(Max Planck Institute, Magdeburg)
Description
Let $f:\Omega\times D\to R$ be some parameterized function with the parameter domain $D$. We develop a sparse empirical quadrature to compute $I(\mu) = \int_\Omega f(x,\mu)dx$. To this end, we compute $I(\mu)$ for a set of training parameters and compute the weights of the quadrature using sparse recovery. At least computationally, we observe that the number of non-zero weights in such a quadrature are bounded by the rank of a snapshot matrix. Since the snapshot matrix of solutions to hyperbolic problems do not have a low rank, we could not preserve the sparsity of the empirical quadrature. Therefore, to retain sparsity, we discuss the possibility of taking the samples of $I(\mu)$ from a calibrated snapshot matrix, which has a low rank.
Primary author
Dr
Neeraj Sarna
(Max Planck Institute, Magdeburg)
