A massively parallel Eikonal solver on unstructured meshes

Abstract

Algorithms for the numerical solution of the Eikonal equation discretized with tetrahedra are discussed. Several massively parallel algorithms for GPU computing are developed. This includes domain decomposition concepts for tracking the moving wave fronts in sub-domains and over the sub-domain boundaries. Furthermore a low memory footprint implementation of the solver is introduced which reduces the number of arithmetic operations and enables improved memory access schemes. The numerical tests for different meshes originating from the geometry of a human heart document the decreased runtime of the new algorithms.

A robust finite element‐finite volume strategy for viscosity‐dominated hydraulic fracture propagation using an asymptotic tip enrichment

“…In order to overcome the above limitations, the Eikonal equation can be solved by using the finite element method, which works both for the structured and unstructured meshes. 65,66 By this way, we can treat the nodal signed distance field as an extra set of primary variables, in addition to the nodal displacement and the cell-centered fluid pressure. Lastly, the current work focuses on modeling the planar fracture that propagates along the internal finite element boundaries.…”

“…However, the nonlinear system requires more iteration steps to converge as shown in the provided numerical examples. In order to overcome the above limitations, the Eikonal equation can be solved by using the finite element method, which works both for the structured and unstructured meshes 65,66 . By this way, we can treat the nodal signed distance field as an extra set of primary variables, in addition to the nodal displacement and the cell‐centered fluid pressure.…”

Multidimensional Information Network Big Data Mining Algorithm Relying on Finite Element Analysis

“…A large number of research results and applications in the field of data analysis and mining can be regarded as an important result of the natural evolution of technology. Strictly speaking, “data mining” usually refers to a broad concept in the industry, which should be more accurately called “mining knowledge from data” or “discovering knowledge from data”; the “data mining” in the strict sense is only a basic work stage in the entire scientific research workflow [ 11 ]. The general process of mining knowledge from data is shown in Figure 2 .…”

Single Pass Computation of First Seismic Wave Travel Time in Three Dimensional Heterogeneous Media With General Anisotropy

“…Other iterative methods include the adaptive Gauss-Siedel iteration [BR06], or the buffered fast marching method [Cri09], which can both handle some amount of anisotropy. Recently, iterative methods which can take advantage of massively parallel computational architecture, graphics processing units (GPU) in particular, have been proposed in the isotropic settings [JW08], and for elliptic anisotropy [GHZ18].…”

“…• Parallelism. The FMM is intrinsically sequential, and thus cannot take advantage of parallel or massively parallel architectures such as [JW08,GHZ18]. • Stencil construction and size.…”