In this paper we present a particle-based method for large scale long time progressive simulation of terrain erosion containing wet granular particles. The wetting process and the propagation through granular material is based on defining the wetness value for each particle representing the amount of water absorbed by granular particles and stored between them, as was originally proposed by Run...

The purpose of these notes is to give some examples illustrating how naive numerical approximations to PDE's may not work at all as expected. In addition, the following two important notions are introduced: (I) von Neumann stability analysis | helps identify when (and if) numerical schemes behave properly. (II) Arti cial viscosity | a tool in stabilizing numerical schemes. These notes should be...

We construct two variable-step linearly implicit Runge–Kutta methods of orders 3 and 4 for the numerical integration of the semidiscrete equations arising after the spatial discretization of advection–reaction–diffusion equations. We study the stability properties of these methods giving the appropriate extension of the concept of L-stability. Numerical results are reported when the methods pre...

Two-step W-methods are linearly implicit time-stepping methods using s external stages that may be processed in parallel. Methods with order s + 1 and stage order s exist. Appropriate generalizations for the concepts of A-and L-stability are derived as well as necessary conditions for A-stability and suucient conditions for stii accuracy. We construct methods of order four where no order reduct...

Datasets are often used multiple times and each successive analysis may depend on the outcome of previous analyses. Standard techniques for ensuring generalization and statistical validity do not account for this adaptive dependence. A recent line of work studies the challenges that arise from such adaptive data reuse by considering the problem of answering a sequence of “queries” about the dat...

A physically-plausible simulation of snow is a challenging task. The method we analyze in this thesis is a Material Point Method (MPM), that has been adjusted to accommodate both the fluid-like and the granular properties of snow. We analyze the simulation in four aspects. One, the noise generated from problems in numerical stability. Two, we analyze the domain in which simulation parameters pe...

In this paper, we study numerically the existence and stability of some special solutions of the nonlinear beam equation: utt +uxxxx +u− |u|p−1u = 0 when p = 3 and p = 5. First we show the existence and the orbital stability of the standing wave solutions: u(x, t) = eφω(x). Next, we study the existence and linear stability of the traveling wave solutions: u(x, t) = φ(x + ct). For both types of ...

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. We present a number of techniques to improve the robustness and efficienc...

In this paper we characterize the set of all restrictions on the behaviour of a plant that shape the characteristic polynomial of the closed-loop system. These control laws include both classical feedback laws and singular feedback laws. One of the results is the behavioural version of the Youla-Jabr-BongiornoKuEera-parameterization of all stabilizing control laws for a given plant. We also stu...