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Q: does it make sense to partially assembled elemental stiffness matrices for affine tetrahedral finite elements when running on a Volta class GPU ? Background: In the reviews of our recent paper on optimizing FEM operations for hexahedral elements we were asked why not assemble the matrices. The comment was an inspiration for this post albeit in this case we are discussing tetrahedral finite elements. A: Recall that we need to compute the following: and the question we are a

BLAS (Basic Linear Algebra Subprograms) is a specification for performing multiple common, basic linear algebra routines. BLAS functions have been implemented and optimized for GPUs, and packaged in libraries (i.e., cuBLAS, CULA, and (batched) MAGMA) . A significant part of the work performed by our finite element codes consists of operations that can be expressed as BLAS routines (i.e., dot products, vector updates, matrix-vector, and matrix-matrix multiplications). We usua

In this post we demonstrate how to optimize the performance of a specific finite element operation expressed as a GPU kernel. One might ask: why are we doing this? Why do we care so much about optimizing performance? After carefully reading this post, it should be clear that there is a substantial difference in performance between basic GPU code and highly optimized GPU code. As our example we use a simple, yet demanding (high arithmetic intensity) matrix-vector kernel coming