
hyper.deal: An efficient, matrixfree finiteelement library for highdimensional partial differential equations
This work presents the efficient, matrixfree finiteelement library hyp...
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Fast matrixfree evaluation of discontinuous Galerkin finite element operators
We present an algorithmic framework for matrixfree evaluation of discon...
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Connections Between Finite Difference and Finite Element Approximations
We present useful connections between the finite difference and the fini...
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Realtime implementation of an iterative solver for atmospheric tomography
The image quality of the new generation of earthbound Extremely Large Te...
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The deal.II finite element library
deal.II is a stateoftheart finite element library focused on generali...
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The deal.II finite element library: design, features, and insights
deal.II is a stateoftheart finite element library focused on generali...
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PVSCDTM: A domainspecific language and matrixfree stencil code for investigating electronic properties of Dirac and topological materials
We introduce PVSCDTM, a highly parallel and SIMDvectorized library and...
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Algorithms and data structures for matrixfree finite element operators with MPIparallel sparse multivectors
Traditional solution approaches for problems in quantum mechanics scale as 𝒪(M^3), where M is the number of electrons. Various methods have been proposed to address this issue and obtain linear scaling 𝒪(M). One promising formulation is the direct minimization of energy. Such methods take advantage of physical localization of the solution, namely that the solution can be sought in terms of nonorthogonal orbitals with local support. In this work a numerically efficient implementation of sparse parallel vectors within the opensource finite element library deal.II is proposed. The main algorithmic ingredient is the matrixfree evaluation of the Hamiltonian operator by cellwise quadrature. Based on an apriori chosen support for each vector we develop algorithms and data structures to perform (i) matrixfree sparse matrix multivector products (SpMM), (ii) the projection of an operator onto a sparse subspace (inner products), and (iii) postmultiplication of a sparse multivector with a square matrix. The nodelevel performance is analyzed using a roofline model. Our matrixfree implementation of finite element operators with sparse multivectors achieves the performance of 157 GFlop/s on Intel Cascade Lake architecture. Strong and weak scaling results are reported for a typical benchmark problem using quadratic and quartic finite element bases.
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