The Application of Domain Decomposition to Time-Domain Computations of Nonlinear Water Waves with a Panel Method

In this paper an iterative domain decomposition method for the solution of Laplace's equation is described and its effectiveness in time-domain computations of nonlinear water waves with a panel method is investigated. An important aspect of these computations is the varying shape of the free surface. The convergence of the iterative method is fast and leads to a speedup of the computations in the aforementioned application. The domain decomposition method gives a considerable reduction of memory requirements. Furthermore, it lends itself naturally for parallel computing

Parallel efficiency of a boundary integral equation method for nonlinear water waves

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on hetero- geneous clusters of workstations is extended to (dedicated) parallel platforms. For these systems a better indication of the parallel performance of the domain decomposition method is obtained because of the absence of varying speed of the processing elements

Numerical simulation of Nonlinear water waves using a panel method: domain decomposition and applications

In studying the influence of water waves on constructions such as dikes, wave breakers and offshore constructions, on ships but also on natural processes such as sediment transport and changes in bottom topography, more and more use is made of numerical models. An important class of such models consists of models in which the flow is described by potential theory. On the one hand the assumptions made in potential theory are valid in many studies, on the other hand the description - its field equation is Laplace's equation for the velocity potential - offers many possibilities for finding solutions with numerical models. The panel method is a numerical method which makes use of a boundary integral formulation for Laplace's equation, so that only the boundaries of the fluid domain have to be covered with grid points. Moreover this enables a natural description of the movement of the free surface in the time domain, which is determined by nonlinear dynamical and kinematical boundary conditions. Nonlinearity of the free-surface boundary conditions is often of importance in studying the influence of waves in coastal and ocean engineering. In this thesis a two-dimensional and three-dimensional numerical model are studied, based on a panel method, for the description of nonlinear water waves. The focus is on two important aspects: firstly the dependence of the computational effort on the number of grid points and secondly some specific numerical difficulties which arise when the method is used in application-like computations. With respect to the former aspect, a domain decomposition technique is studied. The latter aspect is studied for some examples and the suitability and limitations of some parts of the method for these examples are investigated. In more detail the contents of this thesis is as follows. For the domain decomposition technique, an iterative method is chosen in which the domain is divided in the horizontal direction. The length-to-height ratios of the subdomains, among other things, determine the convergence of the iterative method. Because the domains in problems involving water waves generally have large length-to-height ratios, relatively many subdomains can be chosen with a limited loss of convergence. As a consequence the panel method can be applied much more efficiently with domain decomposition. In the case of subdomains with fixed length-to-height ratios, the computational costs per time step depend at most linearly on the length of the domain

Parallel Efficiency of a Boundary Integral Equation Method for Nonlinear Water Waves

Judge Miner\u27s dissent begins on page 153 Matthew Yip appeals from a judgment entered on May 5, 1989 in the United States District Court for the Eastern District of New York (Costantino, J.), convicting him, after a jury trial, of 14 counts of mail fraud in violation of 18 U.S.C. § 1341 (1988), and 59 counts of depriving the United States of lawful duty payments in violation of 18 U.S.C. § 542 (1988). On appeal he contends, inter alia, there was insufficient evidence to support the § 1341 mail fraud convictions, and that the importation of goods using non-fraudulent invoices, followed by the failure to pay customs duties owed on those goods, is not a criminal act within the meaning of § 542. As the principal owner of a customs brokerage house (Airway Shipping), Yip admits he made personal use of funds his clients turned over to him to satisfy their customs obligations to the government. He claims those practices of diverting funds to other businesses and to his own personal use — practices which eventually helped to drive his business into bankruptcy — may have been those of an irresponsible businessman, but did not constitute criminal conduct. The government responds that under the statute all acts that may deprive the Customs agency of duties are made criminal. Our principal task on this appeal is to determine whether the statute is so all-encompassing. We affirm the mail fraud convictions, but reverse the convictions under the customs counts and remand those counts for a new trial