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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Porting hypre to heterogeneous computer architectures: Strategies and experiences

We report that linear systems are occurring in many applications, and solving them can take a large amount of the total simulation time. The high performance library hypre provides a variety of interfaces and linear solvers, including various multigrid methods, that have achieved good scalability on a variety of homogeneous parallel computer architectures. Heterogeneous architectures with nodes that have both CPUs and accelerators provide new challenges, since they require more fine-grained parallelism and reduced data movement between different memories on a single node as well as across nodes. We will discuss our experiences and strategies to port hypre to heterogeneous computers with accelerators, including the design of a new memory model, the use of abstractions, the BoxLoop macros in the structured and semi-structured interfaces, and the restructuring of algebraic multigrid (AMG) into modular components. We present numerical experiments comparing CPU and GPU performance for several test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-Based Algebraic Multigrid (AMGe) Approach

Here, we study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element-agglomeration-based algebraic multigrid (AMGe) technique with improved approximation properties is used, for the first time, to generate upscaled and accurate coarse systems for the reservoir simulation equations. The upscaling technique is applied to both the mixed system for velocity and pressure and to the hyperbolic transport equations, providing fully upscaled systems. By introducing additional degrees of freedom associated with nonplanar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart--Thomas and piecewise discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured and unstructured meshes. Multiscale mixed finite elements exhibit accuracy for general unstructured meshes but do not in general lead to nested hierarchy of spaces. Multiscale multilevel mimetic finite differences generate nested spaces but lack the adaptivity of the flux representation on coarser levels that the proposed AMGe approach offers. Thus, the proposed approach can be seen as a rigorous bridge that merges the best properties of these two existing methods. The accuracy and stability of the studied multilevel AMGe upscaling technique is demonstrated on two challenging test cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Rotational symmetry protected edge and corner states in Abelian topological phases

Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. In this study, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of multiphase flow. We explore the performance of several preconditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “black-box” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. Finally, we show that the new methods are the most robust with respect to problem character, as determined by varying effects of capillary pressures, and we show that the block factorization preconditioner both is efficient and scales optimally with problem size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Accelerating DCA++ (Dynamical Cluster Approximation) Scientific Application on the Summit supercomputer

Optimizing scientific applications on today’s accelerator-based high performance computing systems can be challenging, especially when multiple GPUs and CPUs with heterogeneous memories and persistent non-volatile memories are present. An example is Summit, an accelerator-based system at the Oak Ridge Leadership Computing Facility (OLCF) that is rated as the world’s fastest supercomputer to-date. New strategies are thus needed to expose the parallelism in legacy applications, while being amenable to efficient mapping to the underlying architecture.In this paper we discuss our experiences and strategies to port a scientific application, DCA++, to Summit. DCA++ is a highperformance research application that solves quantum manybody problems with a cutting edge quantum cluster algorithm, the dynamical cluster approximation.Our strategies aim to synergize the strengths of the different programming models in the code. These include: (a) streamlining the interactions between the CPU threads and the GPUs, (b) implementing computing kernels on the GPUs and decreasing CPU-GPU memory transfers, (c) allowing asynchronous GPU communications, and (d) increasing compute intensity by combining linear algebraic operations.Full-scale production runs using all 4600 Summit nodes attained a peak performance of 73.5 PFLOPS with a mixed precision implementation.We observed a perfect strong and weak scaling for the quantum Monte Carlo solver in DCA++, while encountering about 2× input/output (I/O) and MPI communication overhead on the time-to-solution for the full machine run. Our hardware agnostic optimizations are designed to alleviate the communication and I/O challenges observed, while improving the compute intensity and obtaining optimal performance on a complex, hybrid architecture like Summit.

Balduzzi, Giovanni↗
DOE OSTI2020

A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media

Simulation of multiphase poromechanics involves solving a multiphysics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also known as monolithic approaches, are usually preferred. The main bottleneck of a monolithic approach is that it requires solution of large linear systems that result from the discretization and linearization of the governing balance equations. Because such systems are nonsymmetric, indefinite, and highly ill-conditioned, preconditioning is critical for fast convergence. Recently, most efforts in designing efficient preconditioners for multiphase poromechanics have been dominated by physics-based strategies. Current state-of-the-art “black-box” solvers such as algebraic multigrid (AMG) are ineffective because they cannot effectively capture the strong coupling between the mechanics and the flow subproblems, as well as the coupling inherent in the multiphase flow and transport process. In this work, we develop an algebraic framework based on multigrid reduction (MGR) that is suited for tightly coupled systems of PDEs. Using this framework, the decoupling between the equations is done algebraically through defining appropriate interpolation and restriction operators. One can then employ existing solvers for each of the decoupled blocks or design a new solver based on knowledge of the physics. We demonstrate the applicability of our framework when used as a “black-box” solver for multiphase poromechanics. Here, we show that the framework is flexible to accommodate a wide range of scenarios, as well as efficient and scalable for large problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Diagonal and circulant or skew-circulant splitting preconditioners for spatial fractional diffusion equations

We propose three new preconditioners: diagonal and optimal-circulant splitting preconditioner, diagonal and skew-circulant splitting preconditioner, and diagonal and optimal-skew-circulant splitting preconditioner for solving the diagonal-plus-Toeplitz linear system discretized from the spatial fractional diffusion equations. Theoretical analysis shows that these three preconditioners can make the eigenvalues of the preconditioned matrices be clustered around 1, especially when the grids of the discretizations are refined. These results coincide with the one about the diagonal and circulant splitting preconditioner constructed recently by Bai et al. (Numer Linear Algebra Appl 24:e2093, 2017). Numerical experiments exhibit that the proposed preconditioners can significantly improve the convergence of the Krylov subspace iteration methods like GMRES and BiCGSTAB, and they outperform the diagonal and circulant splitting preconditioner as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. In conclusion, for time discretization, Crank–Nicolson scheme and backward Euler scheme are utilized.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem

We investigate the inviscid compressible flow (Euler) equations constrained by an ”isentropic” equation of state (EOS), whose functional form in pressure is an arbitrary function of density alone. Under the aforementioned condition, we interrogate using symmetry methods the scale-invariance of the homentropic inviscid Euler equations. We find that under general conditions, we can reduce the inviscid Euler equations into a system of two coupled ordinary differential equations. To exemplify the utility of these results, we formulate two example scale-invariant, self-similar solutions. The first example includes a shock-free expanding bubble scenario, featuring a modified Tait EOS. The second example features the classical Noh problem, coupled to an arbitrary isentropic EOS. In this case, in order to satisfy the conditions set forth in the classical Noh problem, we find that the solution for the flow is given by a transcendental algebraic equation in the shocked density.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions]

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.

02 PETROLEUM↗
DOE OSTI2024

Robust finite-temperature many-body scarring on a quantum computer

Mechanisms for suppressing thermalization in disorder-free many-body systems, such as Hilbert space fragmentation and quantum many-body scars, have recently attracted much interest in foundations of quantum statistical physics and potential quantum information processing applications. However, their sensitivity to realistic effects such as finite temperature remains largely unexplored. Here, we have utilized IBM's Kolkata quantum processor to demonstrate an unexpected robustness of quantum many-body scars at finite temperatures when the system is prepared in a thermal Gibbs ensemble. We identify such robustness in the PXP model, which describes quantum many-body scars in experimental systems of Rydberg atom arrays and ultracold atoms in tilted Bose-Hubbard optical lattices. By contrast, other theoretical models which host exact quantum many-body scars are found to lack such robustness and their scarring properties quickly decay with temperature. Our study sheds light on the important differences between scarred models in terms of their algebraic structures, which impacts their resilience to finite temperature. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Multigrid is a highly scalable class of methods most often used for solving large linear systems. In this paper we develop a nonlinear algebraic multigrid framework for the power flow equations, a complex quadratic system of the form ${diag}({v})\overline{Y{v}}={s}$, where $Y$ is approximately a complex scalar rotation of a real graph Laplacian. This is a standard problem that needs to be solved repeatedly during power grid simulations. A key difference between our multigrid framework and typical multigrid approaches is the use of a novel multiplicative coarse-grid correction to enable a dynamic multigrid hierarchy. We also develop a new type of smoother that allows one to coarsen together the different types of nodes that appear in power grid simulations. In developing a specific multigrid method, one must make a number of choices that can significantly affect the method's performance, such as how to construct the restriction and interpolation operators, what smoother to use, and how aggressively to coarsen. In this paper, we make simple but reasonable choices that result in a scalable and robust power flow solver. Experiments demonstrate this scalability and show that it is significantly more robust to poor initial guesses than current state-of-the-art solvers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hadamard products and BPS networks

We study examples of fourth-order Picard-Fuchs operators that are Hadamard products of two second-order Picard-Fuchs operators. Each second-order Picard-Fuchs operator is associated with a family of elliptic curves, and the Hadamard product computes period integrals on the fibred product of the two elliptic surfaces. We construct 3-cycles on this geometry as the union of 2-cycles in the fibre over contours on the base. We then use the special Lagrangian condition to constrain the contours on the base. This leads to a construction that is reminiscent of spectral networks and exponential networks that have previously appeared in string theory literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Neutron (and other Particle) Transport at LANL: An Overview [Presentation]

For decades, Los Alamos National Laboratory has been at the forefront of neutron transport methods research and code development. One such code is PARTISN, the LANL parallel time-dependent discrete ordinate neutron transport code. In this presentation, we describe the various research efforts currently underway by the PARTISN and other code teams. Some examples of current research are a block automated mesh refinement scheme, the application of tensor trains to the discretized neutron transport equation, and GPU code porting. The block automated mesh refinement scheme uses cross section information to refine and coarsen the solution mesh to improve time to solution and reduce memory. The tensor train approach expresses discretized transport operators as tensor products of vectors and matrices to compress the size of linear systems being solved by transport codes. Rather than relying on matrix-free methods such as the transport sweep, we have access to an operator that can be inverted, reshaped, or manipulated algebraically. Finally, we describe how PARTISN is used, what problems we are looking to solve, and what the future holds for neutron transport at LANL. In addition to this, we briefly describe the various research efforts in other particle transport teams using both deterministic and Monte Carlo methods. In the presentation, we list possible opportunities for collaboration between the laboratory and faculty and students.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗