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Consistent Second Moment Methods with Scalable Linear Solvers for Radiation Transport
Second moment methods (SMMs) are developed that are consistent with the discontinuous Galerkin spatial discretization of the discrete ordinates (or S\(_N\)) transport equations. The low-order (LO) diffusion system of equations is discretized with fully consistent P\(_1\), local discontinuous Galerkin (LDG), and interior penalty (IP) methods. A discrete residual approach is used to derive SMM correction terms that make each of the LO systems consistent with the high-order discretization. We show that the consistent methods are more accurate and have better solution quality than independently discretized LO systems, that they preserve the diffusion limit, and that the LDG and IP consistent SMMs can be scalably solved in parallel on a challenging, multimaterial benchmark problem.
Extending Petsc's Composable Hierarchically Nested Linear Solvers
The Contributions from the RELACS group at both Rice University and the University at Buffalo in this phase of the PETSc Composable Solvers effort have centered around four main areas: scalable mesh processing, mesh adaptivity, solvers for subsurface flow, and performance modeling. The prominence of mesh processing demonstrates the tight relationship between meshing and discretization on the one hand, and optimal solvers on the other. All optimal solvers that we consider depend on some notion of hierarchy, and we express this using the DMPlex abstraction in PETSc. This relationship demands tight integration between the DM and SNES/TS components in PETSc that is the foundation of much of this work. In addition, interpretation of performance results for scalable solvers necessitates that information from the discretization and solver enter the performance model. Without this, comparing different solvers can be a fruitless exercise. Some major accomplishment of the past three years in these areas include: scalable mesh loading in PETSc on more than 10K cores, integrated mesh adaptivity using both p4est and Pragmatic, scalable multigrid for DG discretizations of subsurface flow, and predictive performance modeling incorporating error estimates.
Innovative applications of block preconditioning and fast linear solvers [Slides]
The goal is to apply principles of linear/nonlinear solvers to lab applications.
Performance portable batched sparse linear solvers in Kokkos kernels.
Abstract not provided.
Performance portable batched sparse linear solvers in Kokkos Kernels.
Abstract not provided.
euroTUG 2023 linear solvers update
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New Linear Solvers Features and Improvements in Trilinos
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Assessing Trilinos Linear Solver Stack Performance Across the DOE Complex
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Why Your Science Application Should Be Using Trilinos Linear Solvers
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An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications
In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.
Linear Solvers for Plasma Simulations on Advanced Architectures.
Abstract not provided.
Incorporating Multiple Compute Precisions into the GMRES Linear Solver.
Abstract not provided.
Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions
Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.