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Davydov, Denis

Publications and source records attributed to Davydov, Denis.

4 records
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DOE OSTI2020

The DEAL.II finite element library: Design, features, and insights

DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, h p -adaptivity, support for complex geometries, and matrix-free algorithms. But DEAL.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

This paper investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. Furthermore, in order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. Additionally, the performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

42 ENGINEERING↗
DOE OSTI2019

DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching ~100,000 electrons) using Kohn-Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn-Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn-Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used plane-wave codes---both in CPU-times and wall-times, and on both non-periodic and periodic systems---at systems sizes beyond a few thousand electrons, with over 5-10 fold speedups in systems with more than 10,000 electrons. In conclusion, the benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated on up to 192,000 MPI tasks.

97 MATHEMATICS AND COMPUTING↗