PETSc Users Manual (Rev. 3.5)

Balay, Satish; Abhyankar, Shrirang; Adams, M.; Brown, Jeremy; Brune, Peter; Buschelman, K.; Eijkhout, Victor; Gropp, William; Kaushik, D.; Knepley, Matthew G.; McInnes, Lois Curfman; Rupp, Karl; Smith, Braeton J.; Zhang, H.

doi:10.2172/1178109

Cited by 387 publications

(380 citation statements)

References 0 publications

Supporting

Mentioning

362

Contrasting

Unclassified

Order By: Relevance

“…The numerical experiments are performed on STAMPEDE [34], a linux cluster hosted by the Texas Advanced Computing Center. The simulations are performed with PETIGA [13], and utilize parallel MUMPS solver [2,3,4] with parallel Scalapack [11] dense solver, parallel SuperLU solver [32,33], and parallel PaStiX solver [23] available from PETSc library [6,7,8]. In the experiments, we utilized one core per Linux cluster node in order to maximize the amount of available memory per node.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The theoretical estimates concerning the computational costs are compared with numerical experiments performed on the STAMPEDE Linux cluster from the Texas Advanced Computing Center [34]. The experiments are performed with the PETIGA toolkit [13] built on the PETSc library [6,7,8], and utilize the parallel MUMPS solver [2,3,4] with parallel Scalapack dense solver [11], the parallel SuperLU solver [32,33], and parallel PaStiX solver [23].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

Woźniak

Paszyński

Pardo

et al. 2015

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

This paper derives theoretical estimates of the computational cost for isogeometric multi-frontal direct solver executed on parallel distributed memory machines. We show theoretically that for the C p−1 global continuity of the isogeometric solution, both the computational cost and the communication cost of a direct solver is of order O(log(N )p 2 ) for the one dimensional (1D) case, O(N p 2 ) for the two dimensional (2D) case, and O(N 4/3 p 2 ) for the three dimensional (3D) case, where N is the number of degrees of freedom and p is the polynomial order of the B-spline basis functions. The theoretical estimates are verified by numerical experiments performed with three parallel multi-frontal direct solvers: MUMPS, PaStiX and SuperLU, available through PETIGA toolkit built on top of PETSc. Numerical results confirm these theoretical estimates both in terms of p and N . For a given problem size, the strong efficiency rapidly decreases as the number of processors increases, becoming about 20 percent for 256 processors for a 3D example with Preprint submitted to Computer Methods in Applied Mechanics and EngineeringNovember 23, 2014 128 3 unknowns and linear B-splines with C 0 global continuity, and 15 percent for a 3D example with 64 3 unknowns and quartic B-splines with C 3 global continuity. At the same time, one cannot arbitrarily increase the problem size, since the memory required by higher order continuity spaces is large, quickly consuming all the available memory resources even in the parallel distributed memory version. Numerical results also suggest that the use of distributed parallel machines is highly beneficial when solving higher order continuity spaces, although the number of processors that one can efficiently employ is somehow limited.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

Woźniak

Paszyński

Pardo

et al. 2015

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…Deal.II expands its functionality by providing interfaces to other packages such as Trilinos, PETSc [6], METIS [15] and others. Each package is added and used via a wrapper class in Deal.II.…”

Section: Implementation Detailsmentioning

confidence: 99%

CPU and GPU Performance of Large Scale Numerical Simulations in Geophysics

Dorostkar

Lukarski

Lund

et al. 2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this work we benchmark the performance of a preconditioned iterative method, used in large scale computer simulations of a geophysical application, namely, the elastic Glacial Isostatic Adjustment model. The model is discretized using the finite element method that gives raise to algebraic systems of equations with matrices that are large, sparse, nonsymmetric, indefinite and with a saddle point structure. The efficiency of solving systems of the latter type is crucial as it is to be embedded in a time-evolution procedure, where systems with matrices of similar type have to be solved repeatedly many times. The implementation is based on available open source software packages -Deal.II, Trilinos, PARALUTION and AGMG. These packages provide toolboxes with state-of-the-art implementations of iterative solution methods and preconditioners for multicore computer platforms and GPU. We present performance results in terms of numerical and the computational efficiency, number of iterations and execution time, and compare the timing results against a sparse direct solver from a commercial finite element package, that is often used by applied scientists in their simulations.

show abstract

“…PERMON extends PETSc [3] with support for quadratic programming (QP) and non-overlapping domain decomposition methods (DDM), namely of the FETI (Finite Element Tearing and Interconnecting) [13,12,5,24] type. This paper presents the process of solving contact problems using PERMON (Section 3).…”

Section: Introductionmentioning

confidence: 99%

Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems lead to inequality constrained quadratic programming problems that can be solved by our PermonQP package.

show abstract

PETSc Users Manual (Rev. 3.5)

Abstract: vii

Cited by 387 publications

References 0 publications

Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines

CPU and GPU Performance of Large Scale Numerical Simulations in Geophysics

Solving Contact Mechanics Problems with PERMON

Contact Info

Product

Resources

About