Related papers: Fast two-scale methods for Eikonal equations
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
$t^*$ represents the total path attenuation and characterizes the amplitude decay of a propagating seismic wave. Calculating the attenuation operator $t^*$ is typically required in seismic attenuation tomography. Traditional methods for…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
We present a method to obtain explicit solutions of the complex eikonal equation in the plane. This equation arises in the approximation of Helmholtz equation by the WKBJ or EWT methods. We obtain the complex-valued solutions (called…
This paper presents a fast wavefield evaluation method for two-dimensional wave scattering problems. The proposed method is based on a modified version of proxy-surface-accelerated interpolative decomposition, making it effective even if…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
This work explores the application of the fast assembly and formation strategy from [8, 17] to trimmed bi-variate parameter spaces. Two concepts for the treatment of basis functions cut by the trimming curve are investigated: one employs a…
Feature selection is one of the most challenging issues in machine learning, especially while working with high dimensional data. In this paper, we address the problem of feature selection and propose a new approach called Evolving Fast and…
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…
Sampling-based planning methods often become inefficient due to narrow passages. Narrow passages induce a higher runtime, because the chance to sample them becomes vanishingly small. In recent work, we showed that narrow passages can be…
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…