Two new methods for simulating photolithography development in 3D

Abstract

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High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

“…Min and Gibou also used the idea of Russo and Smereka with slight modifications in the context of adaptive mesh refinement [90], and Min pointed out that it is advantageous in terms of speed and memory to replace the traditional Runge-Kutta scheme in time with a Gauss-Seidel iteration of the forward Euler scheme [88]. Finally, we mention that other techniques can be used to reinitialize φ as a distance function [125,124,149,166,148,31,147,53], each with their pros and cons. We refer the interested readers to the book by Osher and Fedkiw [101] as well to the book by Sethian [127] for more details on the level-set method.…”

A second order discontinuous Galerkin fast sweeping method for Eikonal equations

“…Among such methods are the fast marching method and the fast sweeping method. The fast marching method [48,43,22,44,45] is based on the Dijkstra's algorithm [18]. The solution is updated by following the causality in a sequential way; i.e., the solution is updated pointwise in the order that the solution is strictly increasing (decreasing); hence two essential ingredients are needed in the algorithm: an upwind difference scheme and a heap-sort algorithm.…”

White matter tractography by anisotropic wavefront evolution and diffusion tensor imaging

“…An efficient single-pass method to solve the Eikonal equation was originally designed by Tsitsiklis (1995) and rediscovered by Helmsen et al (1996) and Sethian (1996) and it is widely known as the FMM. The FMM provides a continuous solution to the shortest-path problem by employing upwind differences and a causality condition.…”