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DOE OSTI2025

SAM User's Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2011

Implementation of the Jacobian-free Newton-Krylov method for solving the for solving the first-order ice sheet momentum balance

We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the rst-order ice sheet momentum equation in order to improve the numerical performance of the Community Ice Sheet Model (CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on signicant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.84-3.62 times more efficient than the standard Picard solver in CISM. Importantly, this computational gain of JFNK over the Picard solver increases when rening the grid. Global convergence of the JFNK solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

PyTrilinos

PyTrilinos is a Python interface to selected Trilinos packages. This makes Trilinos linear algebra classes, linear solvers, preconditioners, nonlinear solvers, eigensolvers, and tools available to Python programmers. This broadens the user base of Trilinos, and facilitates rapid prototyping of scientific codes and interactive manipulation of large, distributed data sets.

Source record↗

DOE OSTI2017

Futility

The Futility package contains the following: 1) Definition of the size of integers and real numbers; 2) A generic Unit test harness; 3) Definitions for some basic extensions to the Fortran language: arbitrary length strings, a parameter list construct, exception handlers, command line processor, timers; 4) Geometry definitions: point, line, plane, box, cylinder, polyhedron; 5) File wrapper functions: standard Fortran input/output files, Fortran binary files, HDF5 files; 6) Parallel wrapper functions: MPI, and Open MP abstraction layers, partitioning algorithms; 7) Math utilities: BLAS, Matrix and Vector definitions, Linear Solver methods and wrappers for other TPLs (PETSC, MKL, etc), preconditioner classes; 8) Misc: random number generator, water saturation properties, sorting algorithms.

Collins, Benjamin S.↗

DOE OSTI2016

An Assessment of Some Design Constraints on Heat Production of a 3D Conceptual EGS Model Using an Open-Source Geothermal Reservoir Simulation Code

Performance of heat production process over a 30-year period is assessed in a conceptual EGS model with a geothermal gradient of 65K per km depth in the reservoir. Water is circulated through a pair of parallel wells connected by a set of single large wing fractures. The results indicate that the desirable output electric power rate and lifespan could be obtained under suitable material properties and system parameters. A sensitivity analysis on some design constraints and operation parameters indicates that 1) the fracture horizontal spacing has profound effect on the long-term performance of heat production, 2) the downward deviation angle for the parallel doublet wells may help overcome the difficulty of vertical drilling to reach a favorable production temperature, and 3) the thermal energy production rate and lifespan has close dependence on water mass flow rate. The results also indicate that the heat production can be improved when the horizontal fracture spacing, well deviation angle, and production flow rate are under reasonable conditions. To conduct the reservoir modeling and simulations, an open-source, finite element based, fully implicit, fully coupled hydrothermal code, namely FALCON, has been developed and used in this work. Compared with most other existing codes that are either closed-source or commercially available in this area, this new open-source code has demonstrated a code development strategy that aims to provide an unparalleled easiness for user-customization and multi-physics coupling. Test results have shown that the FALCON code is able to complete the long-term tests efficiently and accurately, thanks to the state-of-the-art nonlinear and linear solver algorithms implemented in the code.

enhanced geothermal system↗

DOE OSTI2017

Efficient convolutional sparse coding

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

CJW_COMP_WIDGETS v.1.0

Collection of FORTRAN90 routines for software development in finite element analysis using linear nodal and edge basis functions on a tetrahedral mesh. Routines for mesh I/O; mesh quality testing; element-wise mass and stiffness matrix computation, solution I/O; preconditioned iterative linear solvers (QMR, BiCGSTAB and CG) utilizing the matrix-free approach in Weiss (SEG, 2001).

Weiss, Chester J.↗

DOE OSTI2017

HFEM3D

Software solves the three-dimensional Poisson equation div(k(grad(u)) = f, by the finite element method for the case when material properties, k, are distributed over hierarchy of edges, facets and tetrahedra in the finite element mesh. Method is described in Weiss, CJ, Finite element analysis for model parameters distributed on a hierarchy of geometric simplices, Geophysics, v82, E155-167, doi:10.1190/GEO2017-0058.1 (2017). A standard finite element method for solving Poisson’s equation is augmented by including in the 3D stiffness matrix additional 2D and 1D stiffness matrices representing the contributions from material properties associated with mesh faces and edges, respectively. The resulting linear system is solved iteratively using the conjugate gradient method with Jacobi preconditioning. To minimize computer storage for program execution, the linear solver computes matrix-vector contractions element-by-element over the mesh, without explicit storage of the global stiffness matrix. Program output vtk compliant for visualization and rendering by 3rd party software. Program uses dynamic memory allocation and as such there are no hard limits on problem size outside of those imposed by the operating system and configuration on which the software is run. Dimension, N, of the finite element solution vector is constrained by the the addressable space in 32-vs-64 bit operating systems. Total storage requirements for the problem. Total working space required for the program is approximately 13*N double precision words.

Weiss, Chester J↗

DOE OSTI2022

MFIX-Exa: Performance prediction of multiphase energy conversion devices

MFIX-Exa targets the high-fidelity CFD-DEM model in which particles are unresolved by the fluid grid (typically using a fluid mesh approximately twice the particle diameter) but discrete particle dynamics including collisions are resolved with a simple linear-spring dashpot model. The fluid field is solved with a modern low Mach number formation of a cell-centered, nodal-pressure approximate projection method using a Godunov scheme . Physics capabilities include: complex geometries via embedded boundaries (EBs), open and closed system ideal gas equations of state, species transport and heterogeneous chemi- cal reactions. MFIX-Exa is built on the AMReX software framework, the ECP Block-Structured Adaptive Mesh Refinement (AMR) Co-Design Center, which allows the code to be portable and performant.Further integration into the ECP ecosystem includes HYPRE linear solvers and Ascent for in situ visualization. Current project efforts focus on scaling up realistic simulations to the KPP of the challenge problem: NETs 50kW chemical looping reactor, shakedown and scaling on JSLE and OLCF TDS systems and reaching for any remaining performance improvements.

Musser, Jordan↗

DOE OSTI2016

Optimizing a Multiple Right-Hand Side Dslash Kernel for Intel Knights Corner

Lattice Quantum Chromo-dynamics (LQCD) stands unique as the only computationally tractable, non-perturbative, and model-independent quantum field theory of the strong nuclear force. LQCD achieves tractability by discretizing our familiar 4-dimensional space-time onto a hypercubic lattice. The core component of the linear solver used in LQCD is the Wilson-Dirac operator whose finite difference component is called the Dslash operator. Dslash is a nearest neighbor stencil operator summing matrix-vector multiplications over lattice points. The arithmetic intensity of a regular Dslash operator acting on a single vector in single precision is between 0.88-2.29 (depending on the tricks employed) making it memory bandwidth bound on most current architectures, including Xeon Phi. Maximizing the performance of Dslash on Xeon Phi requires deliberate exploitation of its architectural features. One key feature of Xeon Phi is its powerful vector processing unit with lengthy vector registers. There is a class of LQCD computations which aims to solve the Dirac equation for the same lattice gauge fields multiple times. In this case one can gain additional reuse of the gauge field, and potentially simplified vectorization, through applying Dslash to several vectors at the same time; often referred to as Multiple Right Hand Side (MRHS) Dslash. Previous work in this area focused on applying this approach to the Highly Improved Staggered operator, and in cases to the multi-Grid algorithm for Wilson clover fermions. Here, we present two approaches to MRHS Dslash: a vector register blocking approach and one using the software package QPhiX with a custom Code Generator for low-level intrinsics. We explore the Knights Corner instruction set, memory hierarchy, and threading capabilities. For standard lattice sizes used in testing, we observed significant speedups, with sustained performance of over 700 GFLOPS (single precision) in one instance. We achieved up to 27% of theoretical peak performance compared to a maximum of 12% obtained by the previous single RHS method in QPhiX.

Joó, Bálint↗

DOE OSTI2024

Exploiting Power Flow Manifold to Solve AC Optimal Power Flow

AC optimal power flow has proven difficult to solve with interior point methods on GPUs. This is largely due to challenging linear algebra problems that current state of the art massively parallel linear solvers struggle with. However, the advent of Riemannian optimization techniques and the fact that the power flow equations form a smooth manifold present an alternative approach. In this talk, we present the basics of Riemannian optimization techniques in which optimization is done directly on a manifold. Then we present computational results showing that Riemannian techniques are capable of producing solutions of comparable quality as interior point methods.

AC optimal power flow↗

DOE OSTI2020

Scalable Asynchronous Domain Decomposition Solvers

We discuss how parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of low latency network interconnects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Algebraic Multigrid Benchmark

AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.

Yang, Ulrike↗

DOE OSTI2017

Algebraic Multigrid Benchmark

Yang, Ulrike↗

DOE OSTI2013

Algebraic Multigrid Benchmark

AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

Source record↗

DOE OSTI2015

Extending explicit and linearly implicit ODE solvers for index-1 DAEs

Not Available

Lawder, Matthew T.↗

DOE OSTI2019

Innovative Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Numerical simulation of non-isothermal multiphase porous flow combined with reactive transport is used in a wide range of applications, which include nuclear waste repositories, enhanced recovery of petroleum reservoirs, contaminant remediation, geothermal engineering, and carbon sequestration. Understanding and predicting underground phenomena can have enormous impact on how to deal with world issues like climate change, clean water, and renewable energy. The main motivation for this proposal arises from safety assessment of future nuclear waste repositories using the U.S. Department of Energy (DOE) Geologic Disposal Safety Assessment (GDSA) Framework, and performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the nation's only active nuclear waste repository in Carlsbad, New Mexico. I am a technical staff member at Sandia National Laboratories involved in both projects.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗