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This viewgraph presentation covers the advantages of mesh adaptation, unstructured grids, and dynamic load balancing. It illustrates parallel adaptive communications, and explains PLUM (Parallel dynamic load balancing for adaptive unstructured meshes), and PSAW (Proper Self Avoiding Walks).
Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.
We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.
Radiative heat transfer is an important mechanism in a class of challenging engineering and research problems. A direct all-to-all treatment of these problems is prohibitively expensive on large core counts due to pervasive all- to-all MPI communication. The massive heat transfer problem arising from the next generation of clean coal boilers being modeled by the Uintah framework has radiation as a dominant heat transfer mode. Reverse Monte Carlo ray tracing (RMCRT) can be used to solve for the radiative-flux divergence while accounting for the effects of participating media. The ray tracing approach used here replicates the geometry of the boiler on a multi-core node and then uses an all-to-all communication phase to distribute the results globally. The cost of this all-to-all is reduced by using an adaptive mesh approach in which a fine mesh is only used locally, and a coarse mesh is used elsewhere. Here, a model for communication and computation complexity is used to predict performance of this new method. We show this model is consistent with observed results and demonstrate excellent strong scaling to 262K cores on the DOE Titan system on problem sizes that were previously computationally intractable.
Numerical simulation of magnetic systems having corner points is considered. The literature on this topic is reviewed. A method of encapsulating the function behavior near corner points in the difference scheme is proposed for numerical solution of the 2D magnetostatic problem in the iron domain. For the 3D magnetostatic problem in the iron/vacuum domain, the increase in the magnetic field near the corner point is estimated, and a method for construction of an adaptive mesh is proposed. A parallel algorithm is implemented on the graphics-processing unit (GPU) architecture for faster search for the numerical solution of the magnetostatic problem. Numerical simulation is performed for the magnetic system of the SPD detector to be used at the NICA complex (JINR, Dubna).
Emu is a particle-in-cell code for solving the neutrino quantum kinetic equations in 1, 2, or 3 spatial dimensions with arbitrary angular resolution in order to simulate neutrino flavor transformation in neutron star merger and core collapse supernova environments. Emu represents the neutrino distribution function as a set of particles, each of which represent a collection of neutrinos and antineutrinos with unique position and momentum. Each particle carries two density matrices to define the flavor state of the neutrinos and antineutrinos it represents. Emu includes the vacuum, matter, and neutrino self-interaction potentials. Emu calculates the self-interaction potential using PIC deposition and interpolation algorithms that efficiently compute the local number density and flux at particle locations. Emu is implemented in C++ and is based on the AMReX library for high-performance, block-structured adaptive mesh refinement. Emu is parallelized with MPI + OpenMP for CPUs and MPI + CUDA for GPUs.
BoltzmannMFX is a biological simulation code that solves chemical reaction networks using maximum entropy methods. It uses modules from MFiX-Exa and is based on the AMReX framework for massively parallel block-structured adaptive mesh applications.
Critical to the scalability of parallel adaptive simulations are parallel control functions including load balancing, reduced inter-process communication and optimal data decomposition. In distributed meshes, many mesh-based applications frequently access neighborhood information for computational purposes which must be transmitted efficiently to avoid parallel performance degradation when the neighbors are on different processors. This article presents a parallel algorithm of creating and deleting data copies, referred to as ghost copies, which localize neighborhood data for computation purposes while minimizing inter-process communication. The key characteristics of the algorithm are: (1) It can create ghost copies of any permissible topological order in a 1D, 2D or 3D mesh based on selected adjacencies. (2) It exploits neighborhood communication patterns during the ghost creation process thus eliminating all-to-all communication. (3) For applications that need neighbors of neighbors, the algorithm can create n number of ghost layers up to a point where the whole partitioned mesh can be ghosted. Strong and weak scaling results are presented for the IBM BG/P and Cray XE6 architectures up to a core count of 32,768 processors. The algorithm also leads to scalable results when used in a parallel super-convergent patch recovery error estimator, an application that frequently accesses neighborhood data to carry out computation.
This work proposes a new, low-communication algorithm for solving PDEs on massively parallel computers. The range decomposition (RD) algorithm exposes coarse-grain parallelism by applying nested iteration and adaptive mesh refinement locally before performing a global communication step. Just a few such steps are observed to be sufficient to obtain accuracy within a small multiple of discretization error. The target applications are petascale and exascale machines, where hierarchical parallelism is required and traditional parallel numerical PDE communication patterns are costly because of message latency. The RD algorithm uses a partition of unity to equally distribute the error, and thus, the work. The computational advantages of this approach are that the decomposed problems can be solved in parallel without any communication until the partitioned solutions are summed. This offers potential advantages in the paradigm of expensive communication but very cheap computation. This paper introduces the method and explains the details of the communication step. Two performance models are developed, showing that the latency cost associated with a traditional parallel implementation of nested iteration is proportional to log(P) 2 , whereas the RD method reduces the communication latency to log(P), while maintaining similar bandwidth costs. Numerical results for two problems, Laplace and advection diffusion, demonstrate the enhanced performance, and a heuristic argument explains why the method converges quickly.
In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. Here, we develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.
The success of parallel computing in solving real-life computationally-intensive problems relies on their efficient mapping and execution on large-scale multiprocessor architectures. Many important applications are both unstructured and dynamic in nature, making their efficient parallel implementation a daunting task. This paper presents the parallelization of a dynamic unstructured mesh adaptation algorithm using three popular programming paradigms on three leading supercomputers. We examine an MPI message-passing implementation on the Cray T3E and the SGI Origin2OOO, a shared-memory implementation using cache coherent nonuniform memory access (CC-NUMA) of the Origin2OOO, and a multi-threaded version on the newly-released Tera Multi-threaded Architecture (MTA). We compare several critical factors of this parallel code development, including runtime, scalability, programmability, and memory overhead. Our overall results demonstrate that multi-threaded systems offer tremendous potential for quickly and efficiently solving some of the most challenging real-life problems on parallel computers.
AMR-Wind is a massively parallel, block-structured adaptive-mesh, incompressible flow solver for wind turbine and wind farm simulations. The solver is built on top of the AMReX library. AMReX is developed at LBNL , NREL , and ANL as part of the Block-Structured AMR Co-Design Center in DOE's Exascale Computing Project. AMReX library provides the mesh data structures, mesh adaptivity, as well as the linear solvers used for solving the governing equations. The primary applications for AMR-Wind are: performing large-eddy simulations (LES) of atmospheric boundary layer (ABL) flows, simulating wind farm turbine-wake interactions using actuator disk or actuator line models for turbines, and as a background solver when coupled with a near-body solver with overset methodology to perform blade-resolved simulations of multiple wind turbines within a wind farm.
Kynema-SGF (formerly AMR-Wind), wherein SGF stands for structured-grid fluid dynamics, is a massively parallel, block-structured adaptive-mesh, incompressible flow solver. The codebase was initiated in 2019 from incflo. The solver is built on top of the AMReX library. AMReX library provides the mesh data structures, mesh adaptivity, as well as the linear solvers used for solving the governing equations. Kynema-SGF is actively developed and maintained by a dedicated multi-institutional team from Lawrence Berkeley National Laboratory, National Laboratory of the Rockies, and Sandia National Laboratories. The primary applications for Kynema-SGF are: performing large-eddy simulations (LES) of atmospheric boundary layer (ABL) flows, simulating wind farm turbine-wake interactions using actuator disk or actuator line models for turbines, and as a background solver when coupled with a near-body solver (e.g., Kynema-UGF) with overset methodology to perform blade-resolved simulations of multiple wind turbines within a wind farm. For offshore applications, the ability to model the air-sea interaction effects and its impact on the ABL characteristics is another focus for the code development effort. As with other codes in the Kynema ecosystem, Kynema-SGF shares the following objectives: *an open, well-documented implementation of the state-of-the-art computational models for modeling wind farm flow physics at various fidelities that are backed by a comprehensive verification and validation (V&V) process; *be capable of performing the highest-fidelity simulations of flow fields within wind farms; and *be able to leverage the high-performance leadership class computing facilities available at DOE national laboratories.
The evolution of computational methods for crashworthiness and related fields is described and linked with the decreasing cost of computational resources and with improvements in computation methodologies. The latter includes more effective time integration procedures and more efficient elements. Some recent developments in methodologies and future trends are also summarized. These include multi-time step integration (or subcycling), further improvements in elements, adaptive meshes, and the exploitation of parallel computers.
Base heating characteristics is crucial to the success and the overall performance of the X-33 engine. Base heating is important throughout the entire flight trajectory due to the aerospike engine design of X-33. The base region is surrounded by the hot-gas plume, which expands, circulates and impinges on the base. An advanced computation fluid dynamics method is employed in an effort to develop a robust, accurate and efficient tool for the X-33 base heating performance predictions. This computational tool is developed based on a Navier-Stokes flow solver, which is suitable for general complex geometry and includes turbulence, finite-rate chemistry, and radiation models. To fulfill the fast turnaround requirement as a design analysis tool, adaptive mesh refinement method and parallel-computing algorithm are also incorporated in the present model. Case study for the X-33 base-region fluid dynamics and heat transfer characteristics are presented.
This paper presents an examination of the CCA software in sequential and parallel electromagnetics applications using unstructured adaptive mesh refinement.
Dynamic mesh adaption on unstructured grids is a powerful tool for computing unsteady flows that require local grid modifications to efficiently resolve solution features. For this work, we consider an edge-based adaption scheme that has shown good single-processor performance on the C90. We report on our experience parallelizing this code for the SP2. Results show a 47.OX speedup on 64 processors when 10% of the mesh is randomly refined. Performance deteriorates to 7.7X when the same number of edges are refined in a highly-localized region. This is because almost all mesh adaption is confined to a single processor. However, this problem can be remedied by repartitioning the mesh immediately after targeting edges for refinement but before the actual adaption takes place. With this change, the speedup improves dramatically to 43.6X.
In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.