arXiv subjects

Thijs Steel

Publications and source records attributed to Thijs Steel.

7 recordsLinked to original sources

arXiv2026

2D implementation of Kinetic-diffusion Monte Carlo in Eiron

Particle-based kinetic Monte Carlo simulations of neutral particles is one of the major computational bottlenecks in tokamak scrape-off layer simulations. This computational cost comes from the need to resolve individual collision events in high-collisional regimes. However, in such regimes, one can approximate the high-collisional kinetic dynamics with computationally cheaper diffusion. Asymptotic-preserving schemes make use of this limit to perform simulations in these regimes, without a blow-up in computational cost as incurred by standard kinetic approaches. One such scheme is Kinetic-diffusion Monte Carlo. In this paper, we present a first extension of this scheme to the two-dimensional setting and its implementation in the Eiron particle code. We then demonstrate that this implementation produces a significant speedup over kinetic simulations in high-collisional cases.

cs.CE↗

arXiv2025

Fluid boundary conditions in kinetic-diffusion Monte Carlo

The Kinetic-Diffusion Monte Carlo (KDMC) method is a powerful tool for simulating neutral particles in fusion reactors. It is a hybrid fluid-kinetic method that is significantly faster than pure kinetic methods at the cost of a small bias due to fluid approximations. Unfortunately, when simulating particles close to a boundary, it needs to switch to a purely kinetic method, which is significantly slower. In this paper, we will extend the method so that it can accurately take boundary conditions into account without switching to a purely kinetic method. Experiments show that this extension can lead to a speedup of up to 500 times compared to a KDMC method that switches to a purely kinetic method, while not sacrificing too much accuracy.

math.NA↗

arXiv2024

Communication efficient application of sequences of planar rotations to a matrix

We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in three main ways. First, we introduce a new kernel that is optimized for register reuse in a novel way. Second, we introduce a blocking and packing scheme that improves the cache efficiency of the algorithm. Finally, we thoroughly analyze the memory operations of the algorithm which leads to important theoretical insights and makes it easier to select good parameters. Numerical experiments show that our algorithm outperforms the state-of-the-art and achieves a flop rate close to the theoretical peak on modern hardware.

cs.PF↗

arXiv2023

A new deflation criterion for the QZ algorithm

The QZ algorithm computes the Schur form of a matrix pencil. It is an iterative algorithm and at some point, it must decide that an eigenvalue has converged and move on with another one. Choosing a criterion that makes this decision is nontrivial. If it is too strict, the algorithm might waste iterations on already converged eigenvalues. If it is not strict enough, the computed eigenvalues might be inaccurate. Additionally, the criterion should not be computationally expensive to evaluate. This paper introduces a new criterion based on the size of and the gap between the eigenvalues. This is similar to the work of Ahues and Tissuer for the QR algorithm. Theoretical arguments and numerical experiments suggest that it outperforms the most popular criteria in terms of accuracy. Additionally, this paper evaluates some commonly used criteria for infinite eigenvalues.

math.NA↗

arXiv2023

Parallel two-stage reduction to Hessenberg-triangular form

We present a two-stage algorithm for the parallel reduction of a pencil to Hessenberg-triangular form. Traditionally, two-stage Hessenberg-triangular reduction algorithms achieve high performance in the first stage, but struggle to achieve high performance in the second stage. Our algorithm extends techniques described by Karlsson et al. to also achieve high performance in the second stage. Experiments in a shared memory environment demonstrate that the algorithm can outperform state-of-the-art implementations.

cs.DC↗

arXiv2020

A multishift, multipole rational QZ method with aggressive early deflation

The rational QZ method generalizes the QZ method by implicitly supporting rational subspace iteration. In this paper we extend the rational QZ method by introducing shifts and poles of higher multiplicity in the Hessenberg pencil, which is a pencil consisting of two Hessenberg matrices. The result is a multishift, multipole iteration on block Hessenberg pencils which allows one to stick to real arithmetic for a real input pencil. In combination with optimally packed shifts and aggressive early deflation as an advanced deflation technique we obtain an efficient method for the dense generalized eigenvalue problem. In the numerical experiments we compare the results with state-of-the-art routines for the generalized eigenvalue problem and show that we are competitive in terms of speed and accuracy.

math.NA↗

arXiv2019

Pole-swapping algorithms for alternating and palindromic eigenvalue problems

Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic and alternating eigenvalue problems, which arise in control theory, are derived. A refinement step that guarantees backward stability of the algorithms is included. This refinement can also be applied to bulge-chasing algorithms that had been introduced previously, thereby guaranteeing their backward stability in all cases.

math.NA↗