Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “partial differential equation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

MEUMAPPS (Microstructure Evolution Using Massively Parallel Phase-field Simulations)

The software “MEUMAPPS” is a h high-performance computing code used to simulate microstructure evolution associated with diffusional solid-state transformations in structural alloys. Understanding microstructure evolution during thermo-mechanical processing of structural alloys is the first step towards designing and processing alloys for specific applications by meeting property requirements demanded by the application. In this instance, the code is an important component in predicting processing-structure linkages during additive manufacturing of structural alloys as a function of processing parameters and alloy composition used in an additive manufacturing process. The code provides a detailed three-dimensional distribution of different types of phases / constituents and their morphologies, as well as the compositions of these phases that make up the microstructure. The microstructure is simulated by solving the governing partial differential equations using a Fourier Spectral Method.

Radhakrishnan, Balasubram↗
DOE OSTI2022

PsDNS

PsDNS is a Python package which makes it easy to solve partial differential equation using a pseudo-spectral method. The code uses Python classes and Numpy-like arrays to provide a simple interface with which users can construct equations, integrators, and diagnostics. It also includes implementation for common problems, in particular, the incompressible Navier-Stokes equation in a periodic domain, which is commonly used as a benchmark problem for turbulence research. PsDNS uses MPI to allow massively parallel computation for large problems.

Israel, Daniel↗
DOE OSTI2022

DD-AADL

Data Driven Anderson Acceleration for Physics Informed Neural Networks to solve high dimensional partial differential equations

Lupo Pasini, Massimiliano [Oak Ridge National Lab.↗
DOE OSTI2022

Neural Networks for Supercapacitor Modeling

This software implements a one-dimensional model of a supercapacitor and calibrates it to experimental data. A system of coupled partial differential equation models the salt concentration and the ionic and electronic potentials. The term in the equation modeling the capacitance contains a neural network, whose parameters are optimized to fit the provided experimental data. The software is written in python using the open-source library JAX to calculate the gradients needed for the optimization.

Salazar de Troya, Miquel↗
DOE OSTI2021

CARDINAL

Cardinal is a code that automates the workflow for iteratively solving neutral particle transport via the OpenMC code and computational fluid dynamics via the NekRS code within the Multiphysics Object Oriented Simulation Environment (MOOSE), a finite element framework for solving general partial differential equations. Cardinal establishes a mapping between the Monte Carlo geometry representation used in OpenMC and the spectral element mesh used in NekRS to other physics applications built upon the MOOSE framework, allowing high-resolution particle transport and fluid dynamics physics feedback to the MOOSE application ecosystem. Heat generation rates as solved by OpenMC are used as heat sources in MOOSE, while the temperature and density fields from NekRS are used as conjugate heat transfer boundary conditions and/or source fields in MOOSE. OpenMC, Nek5000, and MOOSE are open source, community-developed simulation codes.

NOVAK, APRILJEAN RODGERS↗
DOE OSTI2023

PINNSTRIPES (Physics-Informed Neural Network SurrogaTe for Rapidly Identifying Parameters in Energy Systems) [SWR-22-12]

Energy systems models typically take the form of complex partial differential equations which make multiple forward calculations prohibitively expensive. Fast and data-efficient construction of surrogate models is of utmost importance for applications that require parameter exploration such as design optimization and Bayesian calibration. In presence of a large number of parameters, surrogate models that capture correct dependencies may be difficult to construct with traditional techniques. The issue is addressed here with the formulation of the surrogate model constructed via Physics-Informed Neural Networks (PINN) which capture the dependence with respect to the parameters to estimate, while using a limited amount of data. Since forward evaluations of the surrogate model are cheap, parameter exploration is made inexpensive, even when considering a large number of parameters.

Hassanaly, Malik↗
DOE OSTI2023

LANL contribution to ryujin, an open source finite element solver

Ryujin (https://github.com/conservation-laws/ryujin) is a high-performance finite-element software for solving mathematical partial differential equations (PDEs) with dominant hyperbolic structures. The author of this request, Eric Tovar, is using Ryujin as a high-performance tool for his Mark Kac postdoctoral fellowship research at LANL. Eric would like to contribute openly to the ryujin software without changing its core functionality. This includes: (i) bug fixes; (ii) re-organization of code for performance and syntactic updates including documentation; (iii) implementation of new PDE numerical methods that align with the core solver; (iv) implementation of new initial state configurations for target applications.

Tovar, Eric↗
DOE OSTI2022

Marmot V2

MARMOT is a robust numerical tool for mesoscale modeling of fuel performance developed under the NEAMS Fuels technical area to predict the coevolution of microstructure and properties in fuel and cladding materials. MARMOT accomplishes this using the phase field method coupled with finite strain mechanics and heat conduction. MARMOT is based on the open source Multiphysics Object-Oriented Simulation Environment (MOOSE) and solves the coupled partial differential equations defining the physics using the finite element method. MARMOT is being developed in order to facilitate the development of improved materials models for fuel performance, but it is also being developed as a powerful tool in and of itself for the simulation of mesoscale fuel performance.

Aagesen, LarryK.↗
DOE OSTI2024

AMReX v2024

The software framework, AMReX, supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the essential local descriptions of different physical processes in complex multiphysics algorithms. AMR uses a hierarchical representation of the solution at multiple levels of resolution where the solution on each level is defined on the union of data containers at that resolution. These data containers, which represent the solution over a logically rectangular subregion of the domain, can contain field data defined on a mesh, Lagrangian particles or combinations of both. In addition to these basic data types, AMReX supports a multilevel embedded boundary representation of complex geometry; linear solvers for cell-centered and nodal data; asynchronous I/O in a native format readable by ParaView, VisIt and yt; and interfaces to hypre and PETSc solvers. AMReX enables applications to run on distributed memory architectures with multicore CPUs and with GPU accelerators. AMReX uses a lightweight abstraction layer that effectively hides the details of the architecture from the application. The framework currently supports CUDA, HIP and SYCL for GPU acceleration and OpenMP for multi-core CPU architectures.

Almgren, Ann↗
DOE OSTI2023

Canonical and Noncanonical Hamiltonian Operator Inference

SAND2024-08577O Canonical and Noncanonical Hamiltonian Operator Inference is research code that applies old and new model reduction algorithms to well-known and publicly available "toy" problems. It applies operator inference (OpInf) methods for model reduction to several benchmark hyperbolic partial differential equations: linear wave, Korteweg-de Vries, Benjamin-Bona-Mahoney, and linear elasticity. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2024

Swift

Swift is a fast Fourier transform based spectral solver based on the MOOSE framework. It supports GPU accelerated semi-implicit solves of partial differential equations, such as those used for phase field mesoscale microstructure evolution.

Schwen, Daniel [Idaho National Laboratory (INL), I↗
DOE OSTI2025

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗
DOE OSTI2025

The Method of Finite Averages

The Method of Finite Averages (MoFA) is a rigorous multiscale modeling methodology for efficiently modeling multi-physical phenomena in heterogeneous porous media. The code developed in this project aims to perform the numerical calculations required to formulate, implement, and verify MoFA models for Earth and Energy systems (i.e., model verification refers to performing fully-resolved simulations of the systems and comparing their results to those of the models). In general, MoFA transforms partial differential equations (PDEs) describing the fine-scale physics of a system into coupled ordinary differential equations (ODEs)---in time---that describe the coarse-scale---or "average"---physical behaviors of the system. This transformation significantly expedites system simulation, as the coarse-scale ODEs involve vastly fewer degrees of freedom than the fine-scale PDEs. The code developed under this project will allow users to 1.) generate system geometries and numerical meshes, 2.) solve the PDE and ODE systems required for MoFA model formulation and implementation, 3.) solve the PDE systems required to obtain fully-resolved simulation results for model verification, and 4.) compare and plot results (e.g., the model and fully-resolved simulation solutions, the error between the solutions, etc.).

Pietrzyk, KyleM [Lawrence Livermore National Labor↗
DOE OSTI2026

Fortran mimetic abstraction language (Formal) v0.1.

The Fortran mimetic abstraction language ("Formal") is a domain-specific language (DSL) embedded in Fortran 202Y [1]. Formal provides novel software abstractions for simulating phenomena governed by the partial differential equations (PDEs) of vector and tensor calculus. Such equations model an extremely broad set of physical phenomena, ranging from atmospheric winds to light propagation. Formal's data structures and algorithms mimic in form and behavior continuous functions and operators. Formal supports these mathematical constructs using mimetic discretizations that define a discrete calculus satisfying various tensor calculus theorems, thereby ensuring high-fidelity representations of the physics being modeled. [2] Formal 0.1.0 also lays a foundation for the future use of Fortran 202Y type-safe templates to facilitate the formal verification of tensor contractions in computational physics and artificial intelligence [3]. [1] "Fortran 202Y" is Fortran standard committee's informal designation for the next Fortran revision, which will likely be "Fortran 2028". [2] Corbino, J. and Castillo, J. (2020) Journal of Computational and Applied Mathematics, https://doi.org/10.1016/j.cam.2019.06.042. [3] Haveraaen, M., Järvi, J., & Rouson, D. (2019). Reflecting on Generics for Fortran. https://j3-fortran.org/doc/year/19/19-188.pdf.

Rouson, Damian [Lawrence Berkeley National Laborat↗
DOE OSTI2025

Sparsified Time-dependent PDEs FNO (STFNO) v1.0.0

STFNO (Sparsified Time-dependent PDEs FNO code) is an extension of the popular Fourier Neural Operator (FNO) architecture to the solution of coupled systems of time-dependent partial differential equations. STFNO leverages the sparsified dependencies on the field quantities based on the semi-discretiezed form of the PDEs, enabling significant reduction in the number of model parameters. STFNO has been extensively tested on two fusion simulation codes, NIMROD and GTC, and can be easily tailored to other systems of PDEs.

Rahman, Mustafa [Lawrence Berkeley National Labora↗
DOE OSTI2026

PDEHats

This is code used to train and evaluate neural partial differential equation solvers on an open source fluid flow data. We evaluate two standard deep learning algorithms for their ability to generalize, a desirable capability for trusthworthy and performant models.

Amarel, James↗
DOE OSTI2026

HdsaLib

HdsaLib performs hyper-differential sensitivity analysis in optimization problems that are constrained by partial differential equation problems. The software aids researchers in understanding the impact of uncertainties on their optimization models. The tool has been applied for use in ice sheet modeling, fluid flow modeling, atmospheric tracer transport modeling, and subsurface flow modeling. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

van Bloemen Waanders, Bart [Sandia National Lab. (↗
DOE OSTI2026

qsp4pde v1.0

The software program is a collection of Python implementations of quantum circuits for solving linear partial differential equations using quantum signal processing. The circuits are implemented using the qiskit SDK.

Kim, Hyeongjin [Lawrence Berkeley National Laborat↗