Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the algorithm uses a parallel maximal independent set algorithm in forming aggregates and the resulting coarse level hierarchy is then used in a K-cycle iteration solve phase with a $\ell^1$-Jacobi smoother. Numerical tests of a parallel implementation of the method for graphics processors are presented to demonstrate its effectiveness.Comment: 18 pages, 3 figure

Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond

In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones.Comment: 44 pages. 1 of USQCD whitepapers

Thermodynamic Conditions in Quenching Chamber of Low Voltage Circuit Breaker

Práce se zabývá studiem procesů probíhajících při zhášení silnoproudého oblouku ve zhášecí komoře jističe. Je zaměřena na výpočet dynamiky tekutin a teplotního pole v okolí elektrického oblouku. V práci je dále popsán vliv vzdálenosti plechů v komoře a vliv tvarů plechů z hlediska aerodynamických podmínek uvnitř komory. Dalším cílem dosaženým touto prací je poskytnutí informací o vlivu polohy elektrického oblouku na termodynamické vlastnosti uvnitř komory. Toto je důležité, zejména pokud je oblouk do komory vtahován jinými silami, např. elektromagnetickými a během tohoto vtahovacího procesu mění svůj tvar i polohu. Za účelem co nejjednoduššího, ale zároveň co nejefektivnějšího řešení úkolu, byl vyvinut software určen speciálně pro výpočet dynamiky tekutin numerickou metodou konečných objemů (FVM). Tato metoda je, v porovnání s rozšířenější metodou konečných prvků (FEM), vhodnější pro výpočet dynamiky tekutin (CFD) zejména proto, že režie na výpočet jedné iterace jsou menší v porovnání s ostatními numerickými metodami. Další výhodou tohoto softwarového řešení je jeho modularita a rozšiřitelnost. Cely koncept softwaru je postaven na tzv. zásuvných modulech. Díky tomuto řešení můžeme využít výpočtové jádro pro další numerické analýzy, např. strukturální, elektromagnetickou apod. Jediná potřeba pro úspěšné používání těchto analýz je napsáni solveru pro konečné prvky (FEM). Jelikož je software koncipován jako multi–thread aplikace, využívá výkon současných vícejádrových procesorů naplno. Tato vlastnost se ještě více projeví, pokud se výpočet přesune z CPU na GPU. Jelikož současné grafické karty vyšších tříd mají několik desítek až stovek výpočetních jader a pracují s mnohem rychlejšími pamětmi, než CPU, je výpočetní výkon několikanásobně vyšší.Work deals with the study of processes that attend the electric arc extinction inside the quenching chamber of a circuit breaker. It is focused on several areas. The first one is concerned to fluid dynamics calculations (CFD) and the second one is aimed at thermal field calculations. In this work effects of metal plates distance together with metal plates shapes are described from aerodynamical point of view. Another objective solved by this work is to give information about influence of an electric arc position in a quenching chamber, which changed its shape due to forces acting on it during extinction process. For purpose of this work a new software solution for CFD was developed. Whole software concept is based on plug-ins. Due to this solution, the software§s calculation core can be used for other numerical analyses, like structural, electromagnetic, etc. The only requirement is to write a plug-in for these analyses. Because the software is designed as multi-threaded application, it can use the fully performance of current multi-core processors. Above mentioned property can be especially shown off, when a calculation is moved from CPU to GPU (Graphics Processing Units). Current high-end graphic cards have tens to hundreds cores and work with faster memories than CPU. Due to this fact, the simulation performance can raised manifold.

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in $H({\rm curl})$ and $H({\rm div})$ (e.g. for electromagnetic or radiation diffusion problems) a specially constructed interpolation-histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.Comment: 23 pages, 13 figure

KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners

[EN] Contemporary applications in computational science and engineering often require the solution of linear systems which may be of different sizes, shapes, and structures. The goal of this paper is to explain how two libraries, PETSc and HPDDM, have been interfaced in order to offer end-users robust overlapping Schwarz preconditioners and advanced Krylov methods featuring recycling and the ability to deal with multiple right-hand sides. The flexibility of the implementation is showcased and explained with minimalist, easy-to-run, and reproducible examples, to ease the integration of these algorithms into more advanced frameworks. The examples provided cover applications from eigenanalysis, elasticity, combustion, and electromagnetism.Jose E. Roman was supported by the Spanish Agencia Estatal de Investigacion (AEI) under project SLEPc-DA (PID2019-107379RB-I00)Jolivet, P.; Roman, JE.; Zampini, S. (2021). KSPHPDDM and PCHPDDM: Extending PETSc with advanced Krylov methods and robust multilevel overlapping Schwarz preconditioners. Computers & Mathematics with Applications. 84:277-295. https://doi.org/10.1016/j.camwa.2021.01.0032772958