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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Structured Adaptive Mesh Refinement Adaptations to Retain Performance Portability With Increasing Heterogeneity

Adaptive mesh refinement (AMR) is an important method that enables many mesh-based applications to run at effectively higher resolution within limited computing resources by allowing high resolution only where really needed. This advantage comes at a cost, however: greater complexity in the mesh management machinery and challenges with load distribution. With the current trend of increasing heterogeneity in hardware architecture, AMR presents an orthogonal axis of complexity. Additionally, the usual techniques, such as asynchronous communication and hierarchy management for parallelism and memory that are necessary to obtain reasonable performance are very challenging to reason about with AMR. Different groups working with AMR are bringing different approaches to this challenge. Here, we examine the design choices of several AMR codes and also the degree to which demands placed on them by their users influence these choices.

42 ENGINEERING↗
NASA NTRS1989

Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes

A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.

Batina, John T.↗
NASA NTRS2005

Parallel Adaptive Mesh Refinement Library

Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

Mac-Neice, Peter↗
NASA NTRSDate not supplied

Adaptive mesh refinement and turbulence modeling

Adaptive mesh refinement is shown to be essential in turbulence modeling. Adaptive Mesh Refinement (AMR) is a more computationally efficient means to obtain a discrete approximation to a continuous boundary value problem of a specified accuracy than classic isotropic grid refinement. Previous application of this methodology in the assessment of turbulence models suggested that the field variable solution on the interior of the domain was more sensitive to grid refinement than would be suggested by the sensitivity to grid refinement of surface quantities. Revisiting challenging high speed flow field revealed that issues believed to be fundamental turbulence model issues appear to be related to an under-resolved boundary layer edge – a flow detail previously considered unimportant.

Hypersonics↗
DOE OSTI2022

H-AMR: A New GPU-accelerated GRMHD Code for Exascale Computing with 3D Adaptive Mesh Refinement and Local Adaptive Time Stepping

General relativistic magnetohydrodynamic (GRMHD) simulations have revolutionized our understanding of black hole accretion. Here, we present a GPU-accelerated GRMHD code H-AMR with multifaceted optimizations that, collectively, accelerate computation by 2–5 orders of magnitude for a wide range of applications. First, it introduces a spherical grid with 3D adaptive mesh refinement that operates in each of the three dimensions independently. This allows us to circumvent the Courant condition near the polar singularity, which otherwise cripples high-resolution computational performance. Second, we demonstrate that local adaptive time stepping on a logarithmic spherical-polar grid accelerates computation by a factor of ≲10 compared to traditional hierarchical time-stepping approaches. Jointly, these unique features lead to an effective speed of ~10 9 zone cycles per second per node on 5400 NVIDIA V100 GPUs (i.e., 900 nodes of the OLCF Summit supercomputer). We illustrate H-AMR's computational performance by presenting the first GRMHD simulation of a tilted thin accretion disk threaded by a toroidal magnetic field around a rapidly spinning black hole. With an effective resolution of 13,440 × 4608 × 8092 cells and a total of ≲22 billion cells and ~0.65 × 10 8 time steps, it is among the largest astrophysical simulations ever performed. We find that frame dragging by the black hole tears up the disk into two independently precessing subdisks. The innermost subdisk rotation axis intermittently aligns with the black hole spin, demonstrating for the first time that such long-sought alignment is possible in the absence of large-scale poloidal magnetic fields.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

Lemke, Max↗
DOE OSTI2022

$χ$-$MeRA$: Computationally efficient adaptive mesh refinement of Monte Carlo mesh based tallies

Here, the reactor physics community is always focused on reducing the computational time and memory required for simulations. $χ$-$MeRA$, which stands for flux-based-($χ$)-Mesh tally Refinement Adaptively, was built to reduce the computational time and memory required to solve the neutronics side of a multiphysics problem when compared to traditional methods for mesh based tallies in Monte Carlo (MC) simulations. $χ$-$MeRA$ couples a MC code with an adaptive mesh refinement (AMR) algorithm to take advantage of the accuracy of a MC code and the efficiency of an AMR algorithm. Also developed within $χ$-$MeRA$ was a set of metrics to assess the effects of the refinement on various parameters in the simulation space. For a plutonium sphere, $χ$-$MeRA$ shows a reduction in memory usage and computation time when compared to a fully refined mesh by a factor of 14.7 and 6.7, respectively. When compared to an unstructured mesh, improvement of 1.3 and 4.8 was achieved for memory usage and computation time. The development of $χ$-$MeRA$ helps solve the neutronics side of a multiphysics problem in a faster, more computationally efficient manner than traditional methods, and the final mesh created contains accurate results that can be passed onto the next physics code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

A parallel adaptive mesh refinement algorithm

Over recent years, Adaptive Mesh Refinement (AMR) algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales. In particular, several workers have demonstrated the effectiveness of employing an adaptive, block-structured hierarchical grid system for simulations of complex shock wave phenomena. Unfortunately, from the parallel algorithm developer's viewpoint, this class of scheme is quite involved; these schemes cannot be distilled down to a small kernel upon which various parallelizing strategies may be tested. However, because of their block-structured nature such schemes are inherently parallel, so all is not lost. In this paper we describe the method by which Quirk's AMR algorithm has been parallelized. This method is built upon just a few simple message passing routines and so it may be implemented across a broad class of MIMD machines. Moreover, the method of parallelization is such that the original serial code is left virtually intact, and so we are left with just a single product to support. The importance of this fact should not be underestimated given the size and complexity of the original algorithm.

Quirk, James J.↗
NASA NTRS1999

Adaptive Mesh Refinement for Microelectronic Device Design

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

Cwik, Tom↗
DOE OSTI2019

Adaptive mesh refinement for steady flows in Nek5000

Adaptive mesh refinement is performed in the framework of the spectral element method augmented by approaches to error estimation and control. The h-refinement technique is used for adapting the mesh, where selected grid elements are split by a quadtree (2D) or octree (3D) structure. Continuity between parent-child elements is enforced by high-order interpolation of the solution across the common faces. Parallel mesh partitioning and grid management respectively, are taken care of by the external libraries ParMETIS and p4est. Two methods are considered for estimating and controlling the error of the solution. The first error estimate is local and based on the spectral properties of the solution on each element. This method gives a local measure of the L-2-norm of the solution over the entire computational domain. The second error estimate uses the dual-weighted residuals method - it is based on and takes into account both the local properties of the solution and the global dependence of the error in the solution via an adjoint problem. The objective of this second approach is to optimize the computation of a given functional of physical interest. The simulations are performed by using the code Nek5000 and three steady-state test cases are studied: a two-dimensional lid-driven cavity at Re = 7, 500, a two-dimensional flow past a cylinder at Re = 40, and a three-dimensional lid-driven cavity at Re = 2,000 with a moving lid tilted by an angle of 30 degrees. Finally, the efficiency of both error estimators is compared in terms of refinement patterns and accuracy on the functional of interest. In the case of the adjoint error estimators, the trend on the error of the functional is shown to be correctly represented up to a multiplicative constant.

42 ENGINEERING↗
NASA NTRS2018

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock/Boundary-Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient meansto obtain a discrete approximation to a continuous boundary value problem of a specifiedaccuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW is utilizedto provide estimates of the exact analytical solutions to problems of interest to turbulencemodeling. Predictions of surface pressure and skin friction, essentially the state of stress at thesurface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on theother hand, show marked differences in flows with shocks. The AMR method, as implementedin OVERFLOW2.2k, appears to provide the ability to produce arbitrarily accurate solutionsat a predictable cost much smaller than classic uniform mesh refinement.

Adaptive Mesh Refinement↗
DOE OSTI2021

AMReX: Block-structured adaptive mesh refinement for multiphysics applications

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

Zhang, Weiqun↗
NASA NTRS2001

Highly parallel structured adaptive mesh refinement using parallel language-based approaches

Adaptive mesh refinement (AMR) calculations carried out on structured meshes play an exceedingly important role in several areas of science and engineering. A strategy for using Fortran 90 in an object-oriented fashion is presented. This permits AMR applications to be expressed in terms of familiar abstractions that are natural to the process of solving AMR hierarchies. The OpenMP features that are useful for parallel processing of AMR hierarchies in a load balanced fashion on multiprocessors is described.

computational↗
DOE OSTI2025

Comparison Study of Conventional and Adaptive Mesh Refinement in Organic Material Decomposition Models

This study compares conventional mesh refinement techniques, specifically Uniform Mesh Refinement (UMR), with a new Adaptive Mesh Refinement (AMR) method, applied to Organic Material Decomposition (OMD) models. The proposed benefit of AMR is that only areas that require refinement, based on minimizing a specific field gradient, are refined thus decreasing model wall time compared to conventional UMR methods. This work specifically focuses on comparing UMR and AMR methods on decomposing (both No-Flow and Porous-Flow material models) Polymeric Methylene Diisocyanate (PMDI) polyurethane foam. Throughout the work, the geometry increased in complexity to assess the refinement methods performance at varying levels geometric intricacy. While AMR has been shown to work well in a variety of applications, the UMR approach proved to be computationally faster, for many of the geometries and foam decomposition models, than AMR. However, it was observed that at higher levels of refinement, greater than 3 UMR, AMR begins to be computationally better. Additionally, the settings used to perform AMR greatly impact its performance, and lessons learned, in terms of OMD models, are shared. Due to physics involved in material decomposition, specifically the evolution of state variables, these problems don’t fully benefit from the advantages of AMR.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The Alamo multiphysics solver for phase field simulations with strong-form mechanics and block structured adaptive mesh refinement

Alamo is a high-performance scientific code that uses block-structured adaptive mesh refinement to solve such problems as: the ignition and burn of solid rocket propellant, plasticity, damage and fracture in materials undergoing loading, and the interaction of compressible flow with eroding solid materials. Alamo is powered by AMReX, and provides a set of unique methods, models, and algorithms that enable it to solve solid-mechanics problems (coupled to other physical behavior such as fluid flow or thermal diffusion) using the power of block-structured adaptive mesh refinement.

36 MATERIALS SCIENCE↗
NASA NTRS2018

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock-Boundary Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient means to obtain a discrete approximation to a continuous boundary value problem of a specified accuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW (a computational fluid dynamics (CFD) code) is utilized to provide estimates of the exact analytical solutions to problems of interest to turbulence modeling. Predictions of surface pressure and skin friction, essentially the state of stress at the surface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on the other hand, show marked differences in flows with shocks. The AMR method, as implemented in OVERFLOW 2.2k, appears to provide the ability to produce arbitrarily accurate solutions at a predictable cost much smaller than classic uniform mesh refinement.

Turbulence Modeling↗