A5003911272- Advanced Numerical Methods in Computational Mathematics
- Parallel Computing and Optimization Techniques
- Matrix Theory and Algorithms
- Electromagnetic Simulation and Numerical Methods
- Computational Fluid Dynamics and Aerodynamics
- Advanced Data Storage Technologies
- Distributed and Parallel Computing Systems
- Numerical methods for differential equations
- Numerical methods in engineering
- Electromagnetic Scattering and Analysis
- Computational Geometry and Mesh Generation
- Fluid Dynamics Simulations and Interactions
- Gas Dynamics and Kinetic Theory
- Magnetic confinement fusion research
- Advanced Numerical Analysis Techniques
- Advanced Mathematical Modeling in Engineering
- Lattice Boltzmann Simulation Studies
- 3D Shape Modeling and Analysis
- Computer Graphics and Visualization Techniques
- Tensor decomposition and applications
- Superconducting Materials and Applications
- Manufacturing Process and Optimization
- Scientific Computing and Data Management
- Elasticity and Material Modeling
- Model Reduction and Neural Networks
Lawrence Livermore National Laboratory
2016-2025
Leibniz Supercomputing Centre
2012
Goethe University Frankfurt
2012
Heinz Maier-Leibnitz Zentrum
2012
TU Dresden
2012
Swedish Nuclear Fuel and Waste Management (Sweden)
2012
Gesellschaft für Anlagen und Reaktorsicherheit
2012
Technical University of Darmstadt
2012
Texas A&M University
2001-2005
Institute for Parallel Processing
1999
We consider optimal-scaling multigrid solvers for the linear systems that arise from discretization of problems with evolutionary behavior. Typically, solution algorithms evolution equations are based on a time-marching approach, solving sequentially one time step after other. Parallelism in these traditional time-integration techniques is limited to spatial parallelism. However, current trends computer architectures leading toward more, but not faster, processors. Therefore, faster compute...
The numerical approximation of the Euler equations gas dynamics in a movingLagrangian frame is at heart many multiphysics simulation algorithms. In this paper, we present general framework for high-order Lagrangian discretization these compressible shock hydrodynamics using curvilinear finite elements. This method an extension approach outlined [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated any dimensional kinematic thermodynamic fields,...
This paper investigates the properties of smoothers in context algebraic multigrid (AMG) running on parallel computers with potentially millions processors. The development this case is challenging, because some best relaxation schemes, such as Gauss–Seidel (GS) algorithm, are inherently sequential. Based sharp two-grid theory from [R. D. Falgout and P. S. Vassilevski, SIAM J. Numer. Anal., 42 (2004), pp. 1669–1693] Falgout, L. T. Zikatanov, Linear Algebra Appl., 12 (2005), 471–494] we...
We have investigated the use of adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because FEM is challenging from numerical and computational points view, most published studies in geoelectromagnetics lowest order formulation. Solution resulting large system linear equations poses main practical challenge. developed a fully parallel distributed robust scalable solver based on optimal block-diagonal auxiliary space preconditioners. The was found to be efficient...
As noted in Wikipedia, skin the game refers to having ‘incurred risk by being involved achieving a goal’, where ‘ is synecdoche for person involved, and metaphor actions on field of play under discussion’. For exascale applications development US Department Energy Exascale Computing Project, nothing could be more apt, with delivering comprehensive science-based computational that effectively exploit high-performance computing technologies provide breakthrough modelling simulation data...
In this paper we review a number of auxiliary space based preconditioners for the second order definite and semi-definite Maxwell problems discretized with lowest Nédélec finite elements.We discuss parallel implementation most promising these methods, ones derived from recent Hiptmair-Xu (HX) decomposition [Hiptmair Xu, SIAM J. Numer.Anal., 45 (2007), pp.2483-2509].An extensive set numerical experiments demonstrate scalability our on large-scale H(curl) problems.
In this paper we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), it is implemented open-source package [XBraid: Parallel Multigrid Time, http://llnl.gov/casc/xbraid]. MGRIT scalable and multilevel approach to simulations that nonintrusively uses existing time-stepping schemes, specific two-level setting equivalent widely parareal algorithm. The goal of twofold. First, present analysis linear problems where spatial...
We present a new approach for multi-material arbitrary Lagrangian--Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed curvilinear meshes. The method builds and extends our previous work in the Lagrangian [V. A. Dobrev, T. V. Kolev, R. N. Rieben, SIAM J. Sci. Comput., 34 (2012), pp. B606--B641] remap [R. W. Anderson et al., Internat. Numer. Methods Fluids, 77 (2015), 249--273] phases of ALE, depends critically functional perspective that enables subzonal...
Performance tests and analyses are critical to effective high-performance computing software development central components in the design implementation of computational algorithms for achieving faster simulations on existing future architectures large-scale application problems. In this article, we explore performance space-time trade-offs important compute-intensive kernels numerical solvers partial differential equations (PDEs) that govern a wide range physical applications. We consider...
Abstract We have developed a novel high‐order, energy conserving approach for solving the Euler equations in moving Lagrangian frame, which is derived from general finite element framework. Traditionally, such been solved by using continuous linear representations kinematic variables and discontinuous constant fields thermodynamic variables; this so‐called staggered grid hydro (SGH) method. From our framework, we can derive several specific high‐order discretization methods paper introduce...
In this paper we present a family of scalable preconditioners for matrices arising in the discretization $H(div)$ problems using lowest order Raviart--Thomas finite elements. Our approach belongs to class "auxiliary space''--based methods and requires only element stiffness matrix plus some minimal additional information about topology orientation mesh entities. We provide detailed algebraic description theory, parallel implementation, different variants auxiliary space divergence solver...
We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially many independent where each contraction very small, e.g., sub-vector/warp in size. However, our batch plus application-specifics, we demonstrate close peak performance results. In particular, accelerate large scale tensor-formulated high-order finite element method (FEM) simulations, which the main focus and motivation this work,...
Efficient exploitation of exascale architectures requires rethinking the numerical algorithms used in many large-scale applications. These favor that expose ultra fine-grain parallelism and maximize ratio floating point operations to energy intensive data movement. One few viable approaches achieve high efficiency area PDE discretizations on unstructured grids is use matrix-free/partially-assembled high-order finite element methods, since these methods can increase accuracy and/or lower...
Power and energy consumption are becoming an increasing concern in high performance computing. Compared to multi-core CPUs, GPUs have a much better per watt. In this paper we discuss efforts redesign the most computation intensive parts of BLAST, application that solves equations for compressible hydrodynamics with order finite elements, using Dobrev. exploit hardware parallelism achieve performance, implemented custom linear algebra kernels. We intensively optimized our CUDA kernels by...
We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions Target-Matrix Optimization Paradigm (TMOP) [P. Knupp, Eng. Comput., 28 (2012), pp. 419--429]. This approach allows applications to have very precise control over local mesh quality, while still globally. address adaption various TMOP components settings general isoparametric mappings, including metric in 2D 3D, selection sample points solution resulting optimization...
.In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations the high-order finite element de Rham complex. This theory covers diffusion problems in \(H^1\) , \(\boldsymbol{H}(\mathbf{curl})\) and \(\boldsymbol{H}(\hbox{div})\) is based on combining low-order discretization posed refined mesh with basis Nédélec Raviart–Thomas elements that makes use of concept polynomial histopolation (polynomial fitting using prescribed mean values...