Analog, hybrid, and digital simulation

Analog, hybrid, and digital computerized simulation technique

Bibliography and summary of methods related to the error analysis of hybrid computers technical note no. 4

Bibliography and summary of methods used in error analysis of hybrid computer

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Modelling of radionuclide migration through the geosphere with radial basis function method and geostatistics

The modelling of radionuclide transport through the geosphere is necessary in the safety assessment of repositories for radioactive waste. A number of key geosphere processes need to be considered when predicting the movement of radionuclides through the geosphere. The most important input data are obtained from field measurements, which are not available for all regions of interest. For example, the hydraulic conductivity, as input parameter, varies from place to place. In such cases geostatistical science offers a variety of spatial estimation procedures. To assess the a long term safety of a radioactive waste disposal system, mathematical models are used to describe the complicated groundwater flow, chemistry and potential radionuclide migration through geological formations. The numerical solution of partial differential equations (PDEs) has usually been obtained by finite difference methods (FDM), finite element methods (FEM), or finite volume methods (FVM). Kansa introduced the concept of solving PDEs using radial basis functions (RBFs) for hyperbolic, parabolic and elliptic PDEs. The aim of this study was to present a relatively new approach to the modelling of radionuclide migration through the geosphere using radial basis functions methods and to determine the average and sample variance of radionuclide concentration with regard to spatial variability of hydraulic conductivity modelled by a geostatistical approach. We will also explore residual errors and their influence on optimal shape parameters

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Sampling errors in closed loop hybrid computer programs

Sampling errors in closed loop hybrid computer program

The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundary value problems

Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method

Combining the radial basis function Eulerian and Lagrangian schemes with geostatistics for modeling of radionuclide migration through the geosphere

To assess the long-term safety of a radioactive waste disposal system, mathematical models are used to describe groundwater flow, chemistry, and potential radionuclide migration through geological formations. A number of processes need to be considered, when predicting the movement of radionuclides through the geosphere. The most important input data are obtained from field measurements, which are not available for all regions of interest. For example, the hydraulic conductivity as an input parameter varies from place to place. In such cases, geostatistical science offers a variety of spatial estimation procedures. Methods for solving the solute transport equation can also be classified as Eulerian, Lagrangian and mixed. The numerical solution of partial differential equations (PDE) has usually been obtained by finite-difference methods (FDM), finite-element methods (FEM), or finite-volume methods (FVM). Kansa introduced the concept of solving partial differential equations using radial basis functions (RBF) for hyperbolic, parabolic, and elliptic PDEs. The aim of this study was to present a relatively new approach to the modeling of radionuclide migration through the geosphere using radial basis function methods in Eulerian and Lagrangian coordinates. In this study, we determine the average and standard deviation of radionuclide concentration with regard to variable hydraulic conductivity, which was modelled by a geostatistical approach. Radionuclide concentrations will also be calculated in heterogeneous and partly heterogeneous 2D porous media. (C) 2004 Elsevier Ltd. All rights reserved