It is attractive to combine topology optimization (TO) with additive manufacturing (AM), due to
the design freedom provided by AM, and the increased performance that can be achieved …

We present scalable algorithms for the level-set method on dynamic, adaptive Quadtree and
Octree Cartesian grids. The algorithms are fully parallelized and implemented using the MPI …

The fast marching method is a widely used numerical method for solving the Eikonal
equation arising from a variety of scientific and engineering fields. It is long deemed …

In this paper we present a new algorithm for the solution of Hamilton--Jacobi--Bellman
equations related to optimal control problems. The key idea is to divide the domain of …

Abstract Fast Iterative Method (FIM), a grid-based ray-tracing algorithm, has a computational
efficiency far exceeding that of conventional fast marching method (FMM) in serial …

Numerous applications of Eikonal equations prompted the development of many efficient
numerical algorithms. The Heap-Cell Method (HCM) is a recent serial two-scale technique …

The fast swee** method is a popular algorithm for solving a variety of static Hamilton–
Jacobi equations. Fast swee** algorithms for parallel computing have been developed …

The fast marching method is an essential step in the level set method, widely applied in
seismic tomography. However, there are two key challenges in large-scale seismic …

Numerical solution of the eikonal equation is frequently used to compute first-arrival travel
times for a given velocity model in seismic applications. Computations for large three …

Submarine optical fiber communication cables (subsequently referred to as submarine
cables) form the backbone of the Internet's infrastructure. Damage to these cables can …