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Dobrev, Veselin

Publications and source records attributed to Dobrev, Veselin.

At least 19 records
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DOE OSTI2024

High-performance finite elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. Furthermore, this paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Port and optimize the CEED software stack to Aurora/Frontier EA (ECP Milestone Report)

The goal of this milestone was to port the CEED software stack, including Nek, MFEM and libCEED to the Frontier and Aurora early access hardware, work on optimizing the performance on AMD and Intel GPUs, and demonstrate impact in CEED-enabled ECP applications. As part of this milestone, we also performed a number of other activities, including continued optimizations for CEED applications at scale on Summit, performance evaluation on non-ECP hardware, including the Fugaku’s A64FX chip and the NVIDIA A100 GPU architecture, exploring the use of just-in-time compilations in applications at scale and potential of mixed precision optimizations in the CEED discretization and solver algorithms, and more. During the milestone period, the CEED team released new versions of 6 of its packages, including major releases of MFEM, NekRS and OCCA. We also organized the fifth CEED Annual meeting (CEED5AM) which included nearly 100 researchers from national labs, universities and industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

GPU algorithms for Efficient Exascale Discretizations

In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. Furthermore, we discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm

In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.

42 ENGINEERING↗
DOE OSTI2021

High-order algorithmic developments and optimizations for large-scale GPU-accelerated simulations (Milestone CEED-MS36)

The goal of this milestone was to improve the high-order software ecosystem for CEED-enabled ECP applications by making progress on efficient matrix-free kernels targeting forthcoming ECP architectures. These kernels included matrix-free preconditioning and the development of new set of CEED solver bake-off problems. As part of this milestone, we also released the next version of the CEED software stack, CEED-4.0, reported on results from several application collaborations, and documented the efforts of porting to AMD GPUs for Frontier and other modern architectures, such as Fugaku. The specific tasks addressed in this milestone were: (1) Port and run CEED benchmarks/miniapps on Frontier EA systems; (2) Demonstrate performant libCEED integration in MFEM, Nek and applications; (3) Matrix-free preconditioning of high-order operators; (4) Benchmark problems for fast high-order solvers on GPU platforms; and (5) Public release of CEED-4.0. The artifacts delivered include the next version of the CEED software stack, CEED-4.0, the next libCEED release, libCEED-0.8, and a number of developments integrated within applications to improve their GPU and CPU performance and capabilities. See the CEED website, https://ceed.exascaleproject.org and the CEED GitHub organization, https://github.com/ceed for more details.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Support CEED-enabled ECP applications in their preparation for Aurora/Frontier

The goal of this milestone was to help CEED-enabled ECP applications (particularly ExaSMR, MARBL, ExaAM, ExaWind and E3SM) in their preparations for the Aurora and Frontier architectures. This work included collaboration with ECP vendors and porting and optimization of CEED’s benchmarks and miniapps to early access hardware. As part of this milestone, we also made the best bake-off problems and bake-off kernel implementation from Nek, MFEM, libParanumal and the external community available in the latest libCEED release, libCEED-0.7. During the milestone period we also organized, in virtual form, the fourth CEED Annual meeting (CEED4AM) which included representatives from ECP applications, vendors and software technology projects. The specific tasks addressed in this milestone were to: (1) Work with vendors to port and run CEED benchmarks on early access systems for Aurora and Frontier; (2) Make the best BP/BK implementations from Nek, MFEM, libParanumal and external community available in libCEED; (3) Organize the next CEED Annual meeting (CEED4AM); and (4) Optimize CEED applications and miniapps for Aurora and Frontier architectures. The artifacts delivered include the next libCEED release, libCEED-0.7, and a number of developments integrated within applications to improve their GPU performance and capabilities. See the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed for more details.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scalability of high-performance PDE solvers

Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Simulation-driven optimization of high-order meshes in ALE hydrodynamics

Here we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible shock hydrodynamic applications. The mesh optimization process is driven by information provided by the simulation which uses the optimized mesh, such as shock positions, material regions, known error estimates, etc. These simulation features are usually represented discretely, for instance, as finite element functions on the Lagrangian mesh. The discrete nature of the input is critical for the practical applicability of the algorithms we propose and distinguishes this work from approaches that strictly require analytical information. Our methods are based on node movement through a high-order extension of the Target-Matrix Optimization Paradigm (TMOP). The proposed formulation is fully algebraic and relies only on local Jacobian matrices, so it is applicable to all types of mesh elements, in 2D and 3D, and any order of the mesh. We discuss the notions of constructing adaptive target matrices and obtaining their derivatives, reconstructing discrete data in intermediate meshes, node limiting that enables improvement of global mesh quality while preserving space-dependent local mesh features, and appropriate normalization of the objective function. The adaptivity methods are combined with automatic ALE triggers that can provide robustness of the mesh evolution and avoid excessive remap procedures. The benefits of the new high-order TMOP technology are illustrated on several simulations performed in the high-order ALE application BLAST.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

CEED-MS34: Improve performance and capabilities of CEED-enabled ECP applications on Summit/Sierra. Exascale Computing Project Milestone Report

The main goal of this milestone was to help CEED-enabled ECP applications, including ExaSMR, MARBL, ExaWind and ExaAM, to improve their performance and capabilities on GPU systems like Summit and Lassen/Sierra. In addition, the CEED team also worked to: add and improve support for additional hardware and programming models in the CEED software components; release the next version of the CEED software stack, CEED-3.0; and demonstrate performance of libParanumal kernels in libCEED, Nek and MFEM. These additional tasks contributed directly to the main CEED-MS34 goal and will also play an important role in CEED’s future milestones.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Performance tuning of CEED software and 1st and 2nd wave apps

The goal of this milestone was the performance tuning of the CEED software, as well as the use and tuning of CEED to accelerate the first and second wave of targeted ECP applications. In this milestone, the CEED team developed optimization techniques and tuned for performance the CEED software to accelerate the first and second wave target ECP applications. Specifically, the focus was on the following: (1) Efficient use of the memory sub-system for managing data motion and interactions among different physics packages and libraries; this included integration of the new developments in a libCEED 0.5 software release; (2) Enhancing the CEED libraries with GPU and AMD GPU support in close interaction with vendors; (3) Optimal data locality and motion, and enhanced scalability and parallelism; this included vendors interactions for improvements in data motion and making strong scaling easier and more efficient; and (4) Continue boosting performance for the first-wave and second-wave of ECP target applications, including ExaSMR, ExaWind, Urban, MARBL, E3SM, and ExaAM. A main part of this milestone was the performance tuning of the CEED first-wave and second-wave ECP applications. This included the ExaSMR application – Coupled Monte Carlo Neutronics and Fluid Flow Simulation of Small Modular Reactors (ORNL), the MARBL application – Next-Gen Multi-physics Simulation Code (LLNL), and the ExaAM ExaConstit – a miniapp for the Transforming Additive Manufacturing through Exascale Simulation applications project (ExaAM), as well as ExaWind, Urban, and E3SM. The artifacts delivered include performance improvements in CEED’s 1st and 2nd wave of applications, and tuned CEED software for various architectures through a number of backends, freely available in the CEED’s repository on GitHub. See the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed for more details. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY19 including: CEED’s third annual meeting, MFEM GPU kernels scaling improvements, libCEED 0.5 and NekRS releases, an overview paper covering latest results on a set of bake-off high-order finite element problems (BPs), and other outreach efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

The Target-Matrix Optimization Paradigm for High-Order Meshes

Here, we describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of [P. Knupp, Eng. Comput., 28 (2012), pp. 419--429]. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Lagrangian--Eulerian (ALE) application [BLAST: High-order curvilinear finite elements for shock hydrodynamics, http://www.llnl.gov/CASC/blast]. Our implementation is freely available in an open-source library form [MFEM: Modular parallel finite element methods library, http://mfem.org].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Performance tuning of CEED software and first wave apps

The goal of this milestone was the performance tuning of the CEED software and first wave apps. In this milestone, the CEED team developed optimization techniques and tuned for performance the CEED software. Specifically, the focus was on the following: (1) Fast finite element operator storage and evaluation using partial assembly/matrix-free algorithms that take advantage of tensor-product element structure; (2) Architecture optimizations, including the development of performant discretization libraries targeting heterogeneous systems with multi-core CPUs, GPUs, and/or many-core CPUs in single node, cluster, or large-scale ECP supercomputer configurations; and (3) Global kernels for finite element operators, including the development of algorithms and libraries for fast gather-scatter exchanges for action assembly on unstructured graphs and for components needed for global linear solvers. A main part of this milestone was the performance tuning of the CEED first-wave ECP applications. This included the ExaSMR application – Coupled Monte Carlo Neutronics and Fluid Flow Simulation of Small Modular Reactors (ORNL), and the MARBL application – Next-Gen Multi-physics Simulation Code (LLNL). The artifacts delivered include performance improvements in CEED’s 1st wave of applications, and tuned CEED software for various architectures through a number of backends, freely available in the CEED’s repository on GitHub. See the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed for more details. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY18 including: CEED’s second annual meeting, a successful minisymposium at the premier international conference on high-order methods (ICOSAHOM), making the CEED milestone reports publicly available, new Laghos release, and other outreach efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Initial CEED API (CEED-MS10)

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone, we initiated the development and implementation of a common CEED API consisting of two main components: low-level and high-level APIs. We accomplished the goal of having the low-level component ready for the release of CEED v1.0 in the next quarter, see CEED-MS13. In this report we also provide a highlight from CEED’s integration with the MARBL app and the corresponding Laghos miniapp. A main theme in this work has been the systematic transition of advanced algorithms, developed and tested in Laghos, to the large-scale multi-physics settings of the MARBL code. The low-level CEED API provides a set of FE kernels and components for writing new low-level kernels. Examples include: vector and sparse linear algebra, element matrix assembly over a batch of elements, partial assembly and action for efficient high-order operators like mass, diffusion, advection, etc. The main goal of the low-level API is to establish the basis for the high-level API. Also, identifying such low-level kernels and providing a reference implementation for them serves as the basis for collaboration with vendors and STs. Another goal for the low-level API is to make it easy for applications with their own discretization infrastructure, who do not want to switch directly to using the high-level CEED API, to still evaluate and use the core operations provided by the low-level API. One of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order linear operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for a matvec. Thus, another important question we tried to address while developing the low-level API is: is it possible to abstract out in a natural and efficient way the different implementations and data structures that arise when dealing with various computational device types: CPUs, GPUs, etc. Fully answering this question is beyond the scope of this particular milestone, since that requires longer time as we develop and expand the devices we support. The future high-level API will be the frontend provided by CEED consisting of high-level abstractions such as meshes, finite element spaces and solutions, bilinear forms, solvers, etc. At this high-level, an important aspect of the API will be to provide a uniform abstraction layer for writing code in a portable manner. To achieve that, we plan to utilize the MPI programming model combined with a device abstraction layer (DAL) for finite element computations that we will develop. The DAL will serve as the bridge between the low- and the high-level APIs, allowing a variety of programming models to be used for the low-level kernel implementations. The software artifacts delivered as part of this milestone include an initial CEED API software implementation (libCEED) provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q1 of FY18, including: the Nek5000 v17.0 MFEM v3.3.2 and PETSc v3.8 releases, collaborations with ECP/ST and SciDAC projects, the inaugural Nek5000 hackathon and various outreach activities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

CEED-MS8:Initial Integration of CEED Software in ECP Applications

Key components of CEED software development involve fast finite element operator storage and evaluation, architecture optimizations, performant algorithms for all orders, global kernels for finite element operators, efficient use of the memory sub-system, optimal data locality and motion, enhanced scalability and parallelism, and fast tensor contractions. As ultimate goals of the project, CEED is exploring and identifying the best algorithms for the full range of discretizations and applying algorithmic and software development to support ECP applications’ needs. In this milestone we report on the initial integration of CEED software in the selected first-wave ECP/CEED apps and the continued exploration of other ECP applications as second-wave (milestone CEED-MS23) and third-wave (milestone CEED-MS35) ECP/CEED application candidates. An extensive evaluation of various approaches for GPU acceleration of the CEED computational motives is also a major focus of the report, both in the settings of CEED’s Nekbone and Laghos miniapps, as well as versions of CEED’s bake-off problems (introduced in milestone CEED-MS6). The first-wave ECP applications targeted for coupling with CEED software include the ExaSMR and MARBL applications. We also report on near-term collaboration with the seed-funded Urban Systems project, as well as engagements with ACME, ExaAM, GEOS and the Application Assessment and Proxy App projects. The ExaSMR project involves coupled thermal-hydraulics/neutronics, with the latter based on Monte Carlo methods and the former based on high-order discretizations of the Navier-Stokes and energy equations for accurate simulation of turbulent transport. The project requires fast and efficient turbulence simulation capabilities that will scale to exascale platforms. Work within CEED will ensure that all aspects of the Nek5000 workflow scale to the target problem space, which involves > 10 10 degrees of freedom in typical production runs. CEED’s goal is to provide implementations that perform with maximum attainable efficiency and deliver low turn-around times. A deliverable for this milestone is beta-release of the GPU-based variant of Nek5000. MARBL is targeting high-energy-density physics problems, including single fluid multi-material hydrodynamics and radiation/magnetic diffusion simulation, with applications in inertial confined fusion, pulsed power experiments, and equation of state/material strength analysis. The code uses high-order methods based arbitrary Lagrangian-Eulerian, direct Eulerian, and unstructured adaptive mesh refinement. A deliverable for this milestone is collaboration with MARBL for improved performance based on partially-assembled operators. The Urban exascale project is planning to couple real-time data with high performance simulations to study particulate transport in cities. Nek5000 will be used for large eddy and RANS (Reynolds-averaged Navier-Stokes) simulations of turbulent transport in these domains. Areas where the CEED team is aiding the Urban Canyon group include creating high-order meshes for urban geometries and developing boundary conditions appropriate for simulations close to real-life urban conditions. The software artifacts delivered as part of this milestone include GPU-enabled versions of the Nekbone and Laghos miniapps, which are provided through the CEED website, http://ceed.exascaleproject.org and the CEED GitHub organization, http://github.com/ceed. In addition to details and results from the above R&D efforts, in this document we are also reporting on other project-wide activities performed in Q4 of FY17, including: the CEED first annual meeting and participation of CEED researchers in a variety of outreach activities.

97 MATHEMATICS AND COMPUTING↗