A GPU-accelerated adaptive discontinuous Galerkin method for level set equation

2016-01-02
KARAKUS, A.
WARBURTON, T.
AKSEL, MEHMET HALUK
Sert, Cüneyt
This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams-Bashforth scheme. Platform independence of the solver is achieved with an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable, accurate and mass conservative numerical scheme that preserves the simplicity of LS formulation is obtained. Efficiency, performance and local high-order accuracy of the method are demonstrated through distinct numerical test cases.
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS

Suggestions

A local discontinuous Galerkin level set reinitialization with subcell stabilization on unstructured meshes[Formula presented]
Karakuş, Ali; Chalmers, N.; Warburton, T. (2022-10-01)
© 2022 Elsevier LtdIn this paper we consider a level set reinitialization technique based on a high-order, local discontinuous Galerkin method on unstructured triangular meshes. A finite volume based subcell stabilization is used to improve the nonlinear stability of the method. Instead of the standard hyperbolic level set reinitialization, the flow of time Eikonal equation is discretized to construct an approximate signed distance function. Using the Eikonal equation removes the regularization parameter in...
A stagnation-aware cooperative parallel breakout local search algorithm for the quadratic assignment problem
Aksan, Yagmur; Dokeroglu, Tansel; Coşar, Ahmet (2017-01-01)
The Quadratic Assignment Problem (QAP) is one of the most challenging NP-Hard combinatorial optimization problems. Circuit-layout design, transportation/traffic engineering, and assigning gates to airplanes are some of the interesting applications of the QAP. In this study, we introduce an enhanced version of a recent local search heuristic, Breakout Local Search Algorithm (BLS), by using the Levenshtein Distance metric for checking the similarity of the new starting points to previously explored QAP permut...
A Novel Alternating Cell Directions Implicit Method for the Solution of Incompressible Navier Stokes Equations on Unstructured Grids
Bas, O.; ÇETE, ALİ RUHŞEN; Mengi, S.; Tuncer, İsmail Hakkı; Kaynak, U. (2017-01-01)
In this paper, A Novel Alternating Cell Direction Implicit Method (ACDI) is researched which allows implementation of fast line implicit methods on quadrilateral unstructured meshes. In ACDI method, designated alternating cell directions are taken along a series of contiguous cells within the unstructured grid domain and used as implicit lines similar to Line Gauss Seidel Method (LGS). ACDI method applied earlier for the solution of potential flows is extended for the solution of the incompressible Navier-S...
A local discontinuous Galerkin method for Dirichlet boundary control problems
Yücel, Hamdullah (null; 2018-10-20)
In this paper, we consider Dirichlet boundary control of a convection-diffusion equation with L 2 4 – 5 boundary controls subject to pointwise bounds on the control posed on a two dimensional convex polygonal domain. 6 We use the local discontinuous Galerkin method as a discretization method. We derive a priori error estimates for 7 the approximation of the Dirichlet boundary control problem on a polygonal domain. Several numerical results are 8 provided to illustrate the theoretical results.
A GPU ACCELERATED NODAL DISCONTINUOUS GALERKIN SOLVER FOR THE SOLUTION OF LATTICE-BOLTZMANN EQUATIONS ON UNSTRUCTURED MESHES
Karakuş, Ali (2022-05-27)
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Lattice-Boltzmann equations on unstructured triangular and quadrilateral meshes. The equations are discretized in time using semi-analytic time integration scheme enabling higher CFL numbers in stiff regimes. Performance portability of the solver on different platforms is achieved by using the open concurrent compute abstraction, OCCA. We optimize the performance of the most time-consuming ker...
Citation Formats
A. KARAKUS, T. WARBURTON, M. H. AKSEL, and C. Sert, “A GPU-accelerated adaptive discontinuous Galerkin method for level set equation,” INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS, pp. 56–68, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35798.