Related papers: MPI-AMRVAC: a parallel, grid-adaptive PDE toolkit
Computational magnetohydrodynamics (MHD) for space physics has become an essential area in understanding the multiscale dynamics of geophysical and astrophysical plasma processes, partially motivated by the lack of space data. Full MHD…
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…
The chromosphere is a partially ionized layer of the solar atmosphere, the transition between the photosphere where the gas is almost neutral and the fully ionized corona. As the collisional coupling between neutral and charged particles…
Advances in detectors and computational technologies provide new opportunities for applied research and the fundamental sciences. Concurrently, dramatic increases in the three Vs (Volume, Velocity, and Variety) of experimental data and the…
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…
Optimizing high-performance power electronic equipment, such as power converters, requires multiscale simulations that incorporate the physics of power semiconductor devices and the dynamics of other circuit components, especially in…
The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use…
The alternating direction method of multipliers (ADMM) has gained increasing popularity in embedded model predictive control (MPC) due to its code simplicity and pain-free parameter selection. However, existing ADMM solvers either target…
A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
Afivo is a framework for simulations with adaptive mesh refinement (AMR) on quadtree (2D) and octree (3D) grids. The framework comes with a geometric multigrid solver, shared-memory (OpenMP) parallelism and it supports output in Silo and…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…
Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical…
The long-term success of climate models that operate on multi-resolution grids will depend on access to subgrid parameterizations that act appropriately across a wide range of spatial and temporal scales. As the first step in a series of…
[Devito] is an open-source Python project based on domain-specific language and compiler technology. Driven by the requirements of rapid HPC applications development in exploration seismology, the language and compiler have evolved…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…
The high computational demands of multiscale modeling necessitate advanced parallel and adaptive strategies. To address this challenge, we introduce an adaptive method that utilizes two microscale models based on an offline database for…
A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…