Jacob Moore

We introduce a Lagrangian nodal discontinuous Galerkin (DG) cell-centered hydrodynamics method for solving multi-dimensional hyperbolic systems. By incorporating an adaptation of Zalesak's flux-corrected transport algorithm, we combine a first-order positivity-preserving scheme with a higher-order target discretization. This results in a flux-corrected Lagrangian DG scheme that ensures both global positivity preservation and second-order accuracy for the cell averages of specific volume. The correction factors for flux limiting are derived from specific volume and applied to all components of the solution vector. We algebraically evolve the volumes of mesh cells using a discrete version of the geometric conservation law (GCL). The application of a limiter to the GCL fluxes is equivalent to moving the mesh using limited nodal velocities. Additionally, we equip our method with a locally bound-preserving slope limiter to effectively suppress spurious oscillations. Nodal velocity and external forces are computed using a multidirectional approximate Riemann solver to maintain conservation of momentum and total energy in vertex neighborhoods. Employing linear finite elements and a second-order accurate time integrator guarantees GCL consistency. The results for standard test problems demonstrate the stability and superb shock-capturing capabilities of our scheme.

Efficiently simulating solid mechanics is vital across various engineering applications. As constitutive models grow more complex and simulations scale up in size, harnessing the capabilities of modern computer architectures has become essential for achieving timely results. This paper presents advancements in running parallel simulations of solid mechanics on multi-core CPUs and GPUs using a single-code implementation. This portability is made possible by the C++ matrix and array (MATAR) library, which interfaces with the C++ Kokkos library, enabling the selection of fine-grained parallelism backends (e.g., CUDA, HIP, OpenMP, pthreads, etc.) at compile time. MATAR simplifies the transition from Fortran to C++ and Kokkos, making it easier to modernize legacy solid mechanics codes. We applied this approach to modernize a suite of constitutive models and to demonstrate substantial performance improvements across different computer architectures. This paper includes comparative performance studies using multi-core CPUs along with AMD and NVIDIA GPUs. Results are presented using a hypoelastic–plastic model, a crystal plasticity model, and the viscoplastic self-consistent generalized material model (VPSC-GMM). The results underscore the potential of using the MATAR library and modern computer architectures to accelerate solid mechanics simulations.

This paper presents software advances to easily exploit computer architectures consisting of a multi-core CPU and CPU+GPU to accelerate diverse types of high-performance computing (HPC) applications using a single code implementation. The paper describes and demonstrates the performance of the open-source C++ matrix and array (MATAR) library that uniquely offers: (1) a straightforward syntax for programming productivity, (2) usable data structures for data-oriented programming (DOP) for performance, and (3) a simple interface to the open-source C++ Kokkos library for portability and memory management across CPUs and GPUs. The portability across architectures with a single code implementation is achieved by automatically switching between diverse fine-grained parallelism backends (e.g., CUDA, HIP, OpenMP, pthreads, etc.) at compile time. The MATAR library solves many longstanding challenges associated with easily writing software that can run in parallel on any computer architecture. This work benefits projects seeking to write new C++ codes while also addressing the challenges of quickly making existing Fortran codes performant and portable over modern computer architectures with minimal syntactical changes from Fortran to C++. We demonstrate the feasibility of readily writing new C++ codes and modernizing existing codes with MATAR to be performant, parallel, and portable across diverse computer architectures.

The U.S. Department of Energy's Office of Scientific and Technical Information