Related papers: Improved Fast Iterative Algorithm for Eikonal Equa…
Numerical solutions to the Eikonal equation are computed using variants of the fast marching method, the fast sweeping method, and the fast iterative method. In this paper, we provide a unified view of these algorithms that highlights their…
The fast marching method is well-known for its worst-case optimal computational complexity in solving the Eikonal equation, and has been employed in numerous scientific and engineering fields. However, it has barely benefited from…
A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update…
We present a family of fast and accurate Dijkstra-like solvers for the eikonal equation and factored eikonal equation which compute solutions on a regular grid by solving local variational minimization problems. Our methods converge…
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 inherently sequential and an efficient parallel algorithm applicable…
The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM)…
The Fast Marching Method is a very popular algorithm to compute times-of-arrival maps (distances map measured in time units). Since their proposal in 1995, it has been applied to many different applications such as robotics, medical…
This paper presents an efficient parallel Adaptive Inverse Distance Weighting (AIDW) interpolation algorithm on modern Graphics Processing Unit (GPU). The presented algorithm is an improvement of our previous GPU-accelerated AIDW algorithm…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Fast Marching and Fast Sweeping are the two most commonly used methods for solving the Eikonal equation. Each of these methods performs best on a different set of problems. Fast Sweeping, for example, will outperform Fast Marching on…
We introduce a fast Eikonal Phase Retrieval (EPR) formulation that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second-order asymptotic expansion…
We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion,…
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…
The recent deep learning revolution has created an enormous opportunity for accelerating compute capabilities in the context of physics-based simulations. Here, we propose EikoNet, a deep learning approach to solving the Eikonal equation,…
This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…
Aitken extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition…
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…