arXiv subjects

Mikhail Kirilin

Publications and source records attributed to Mikhail Kirilin.

3 recordsLinked to original sources

arXiv2025

A new Dune grid for scalable dynamic adaptivity based on the p4est software library

In this work we extend the Dune solver library with another grid interface to the open-source p4est software. While Dune already supports about a dozen different mesh implementations through its mesh interface Dune-Grid, we undertake this new coupling effort in order to inherit p4est's practically unlimited MPI scalability as well as its relatively thin data structures, and its native support for multi-block (forest) mesh topologies in both 2D and 3D. The presented implementation is compared to an existing implementation based on Dune-ALUGrid for a variety of challenging test examples in a parallel environment. The numerical experiments show that the implementation presented here is outperforming Dune-ALUGrid in terms of scalability. In addition, an alternative balancing strategy is presented to ensure 2:1 balancing across element faces showing improved performance compared to the existing p4est balance strategy in the numerical examples considered in this work.

cs.DC↗

arXiv2025

Convergence of generalized cross-validation with applications to ill-posed integral equations

In this article, we rigorously establish the consistency of generalized cross-validation as a parameter-choice rule for solving inverse problems. We prove that the index chosen by leave-one-out GCV achieves a non-asymptotic, order-optimal error bound with high probability for polynomially ill-posed compact operators. Hereby it is remarkable that the unknown true solution need not satisfy a self-similarity condition, which is generally needed for other heuristic parameter choice rules. We quantify the rate and demonstrate convergence numerically on integral equation test cases, including image deblurring and CT reconstruction.

math.NA↗

arXiv2023

Alternative quadrant representations with Morton index and AVX2 vectorization for AMR algorithms within the p4est software library

We present a technical enhancement within the p4est software for parallel adaptive mesh refinement. In p4est primitives are stored as octants in three and quadrants in two dimensions. While, classically, they are encoded by the native approach using its spatial and refinement level, any other mathematically equivalent encoding might be used instead. Recognizing this, we add two alternative representations to the classical, explicit version, based on a long monotonic index and 128-bit AVX quad integers, respectively. The first one requires changes in logic for low-level quadrant manipulating algorithms, while the other exploits data level parallelism and requires algorithms to be adapted to SIMD instructions. The resultant algorithms and data structures lead to higher performance and lesser memory usage in comparison with the standard baseline. We benchmark selected algorithms on a cluster with two Intel(R) Xeon(R) Gold 6130 Skylake family CPUs per node, which provides support for AVX2 extensions, 192 GB RAM per node, and up to 512 computational cores in total.

cs.MS↗