Related papers: Efficient Multigrid Preconditioners for Atmospheri…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
In this article we introduce a novel coupled algorithm for massively parallel direct numerical simulations of electrophoresis in microfluidic flows. This multiphysics algorithm employs an Eulerian description of fluid and ions, combined…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver…
We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {\ttfamily deal.II} library. It addresses both high-order…
Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…
Pressure projection is the single most computationally expensive step in an unsteady incompressible fluid simulation. This work demonstrates the ability of data-driven methods to accelerate the approximate solution of the Poisson equation…
We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…
An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element and fast execution speed. The code is based on a…
Elliptic equations play a crucial role in turbulence models for magnetic confinement fusion. Regardless of the chosen modeling approach - whether gyrokinetic, gyrofluid, or drift-fluid - the Poisson equation and Amp\`{e}re's law lead to…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
Despite the extensive application of nonlinear Model Predictive Control (MPC) in automated driving, balancing its computational efficiency with respect to the control performance and constraint satisfaction remains a challenge in emergency…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…
This paper presents a large-scale parallel solver, specifically designed to tackle the challenges of solving high-dimensional and high-contrast linear systems in heat transfer topology optimization. The solver incorporates an interpolation…