Many simulation problems can be described using hyperbolic partial differential equations. Solving these with performance in mind while not sacrificing too much in terms of accuracy can be achieved using refined numerical solvers, such as ADER-DG.

ExaHyPE 2 can generate sophisticated C++ code that uses ADER-DG to solve such numerical problems. It often requires many matrix multiplications, so providing an optimized implementation for them can be very beneficial to performance. This is currently done using an older version of the libxsmm code generator driver, which is deprecated, so we explore the use of another implementation: BLIS. During testing, we find that BLIS is not as performant for the smaller matrix multiplications used throughout most problems. On the grounds of this, we also take into consideration Eigen and a newer version of libxsmm that generates code during runtime to determine whether they can achieve performance that is comparable to or better than the existing option.

We explore the performance of all four implementations in exhaustive isolated performance tests with various matrix sizes and environments. During these tests we observe that Eigen and the newer libxsmm version can outperform the existing implementation in certain realistically occurring situations, mainly when the existing implementation does not provide optimizations for the specific microarchitecture. As a result of that and the fact that BLIS may become more performant for smaller matrix multiplications in the future, we incorporate all three of the newly explored implementations in the ExaHyPE 2 generator as an addition to the one that is already included. Consequentially, users of ExaHyPE 2 can easily have such optimizations included in their generated ADER-DG programs by invoking an option.

In performance tests on the entire program, we find that Eigen may sometimes outperform the previously used libxsmm code generator driver, even in cases where it is optimized for the underlying microarchitecture.