相关论文: Towards a Scalable Hierarchical High-order CFD Sol…
The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…
Deep learning solvers for partial differential equations typically have limited accuracy. We propose to overcome this problem by using them as preconditioners. More specifically, we apply discretization-invariant neural operators to learn…
In this paper we propose a new spatially high order accurate semi-implicit discontinuous Galerkin (DG) method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured curved meshes. While the…
We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…
We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and…
The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…
In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…
We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells…
In this paper, we present an interior penalty discontinuous Galerkin finite element scheme for solving diffusion problems with strong anisotropy arising in magnetized plasmas for fusion applications. We demonstrate the accuracy produced by…
The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at…
We investigate the ability of discontinuous Galerkin (DG) methods to simulate under-resolved turbulent flows in large-eddy simulation. The role of the Riemann solver and the subgrid-scale model in the prediction of a variety of flow…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
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…
In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…
Computational advances have fundamentally transformed the landscape of numerical simulations, enabling unprecedented levels of complexity and precision in modeling physical phenomena. While these high-fidelity simulations offer invaluable…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the…