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1 
Use of isotropic fundamental solutions for solving anisotropic problemsPerez, Mario Mourelle January 1993 (has links)
No description available.

2 
A multifrequency method for the solution of the acoustic inverse scattering problemBorges, Carlos 08 January 2013 (has links)
We are interested in solving the timeharmonic inverse acoustic scattering problem for planar soundsoft obstacles. In this work, we introduce four methods for solving inverse scattering problems. The first method is a variation of the method introduced by Johansson and Sleeman. This method solves the inverse problem when we have the far field pattern given for only one incident wave. It is an iterative method based on a pair of integral equations used to obtain the far field pattern of a known single object. The method proposed in this thesis has a better computational performance than the method of Johansson and Sleeman. The second method we present is a multifrequency method called the recursive linearization algorithm. This method solves the inverse problem when the far field pattern is given for multiple frequencies. The idea of this method is that from an initial guess, we solve the single frequency inverse problem for the lowest frequency. We use the result obtained as the initial guess to solve the problem for the next highest frequency. We repeat this process until we use the data from all frequencies. To solve the problem at each frequency, we use the first method proposed. To improve the quality of the reconstruction of the shadowed part of the object, we solve the inverse scattering problem of reconstructing an unknown soundsoft obstacle in the presence of known scatterers. We show that depending on the position of the scatterers, we may be able to obtain very accurate reconstructions of the entire unknown object. Next, we introduce a method for solving the inverse problem of reconstructing a convex soundsoft obstacle, given measures of the far field pattern at two frequencies that are not in the resonance region of the object. This method is based on the use of an approximation formula for the far field pattern using geometric optics. We are able to prove that for the reconstruction of the circle of radius $R$ and center at the origin, the size of the interval of convergence of this method is proportional to the inverse of the wavenumber. This procedure is effective at reconstructing the illuminated part of the object; however, it requires an initial guess close to the object for frequencies out of the resonance region. Finally, we propose a globalization technique to obtain a better initial guess to solve the inverse problem at frequencies out of the resonance region. In this technique, given the far field pattern of a convex object at two frequencies out of the resonance region, we use our extrapolation operator to generate synthetic data for low frequencies. We apply the recursive linearization algorithm, using as a single frequency solver the method that is based on geometric optics. We obtain an approximation of the object that can be used as the initial guess to apply the recursive linearization algorithm using the first method introduced as the single frequency solver.

3 
A numerical method based on RungeKutta and GaussLegendre integration for solving initial value problems in ordinary differential equationsPrentice, Justin Steven Calder 11 September 2012 (has links)
M.Sc. / A class of numerical methods for solving nonstiff initial value problems in ordinary differential equations has been developed. These methods, designated RKrGLn, are based on a RungeKutta method of order r (RKr), and GaussLegendre integration over n+ 1 nodes. The interval of integration for the initial value problem is subdivided into an integer number of subintervals. On each of these n + 1 nodes are defined in accordance with the zeros of the Legendre polynomial of degree n. The RungeKutta method is used to find an approximate solution at each of these nodes; GaussLegendre integration is used to find the solution at the endpoint of the subinterval. The process then carries over to the next subinterval. We find that for a suitable choice of n, the order of the local error of the Runge Kutta method (r + 1) is preserved in the global error of RKrGLn. However, a poor choice of n can actually limit the order of RKrGLn, irrespective of the choice of r. What is more, the inclusion of GaussLegendre integration slightly reduces the number of arithmetical operations required to find a solution, in comparison with RKr at the same number of nodes. These two factors combine to ensure that RKrGLn is considerably more efficient than RKr, particularly when very accurate solutions are sought. Attempts to control the error in RKrGLn have been made. The local error has been successfully controlled using a variable stepsize strategy, similar to that generally used in RK methods. The difference lies in that it is the size of each subinterval that is controlled in RKrGLn, rather than each individual stepsize. Nevertheless, local error has been successfully controlled for relative tolerances ranging from 10 4 to 1010 . We have also developed algorithms for estimating and controlling the global error. These algorithms require that a complete solution be obtained for a specified distribution of nodes, after which the global error is estimated and then, if necessary, a new node distribution is determined and another solution obtained. The algorithms are based on Richardson extrapolation and the use of loworder and highorder pairs. The algorithms have successfully achieved desired relative global errors as small as 101° . We have briefly studied how RKrGLn may be used to solve stiff systems. We have determined the intervals of stability for several RKrGLn methods on the real line, and used this to develop an algorithm to solve a stiff problem. The algorithm is based on the idea of stepsize/subinterval adjustment, and has been used to successfully solve the van der Pol system. Lagrange interpolation on each subinterval has been implemented to obtain a piecewise continuous polynomial approximation to the numerical solution, with same order error, which can be used to find the solution at arbitrary nodes.

4 
Computation and Numerics in NeurostimulationDougherty, Edward T. 07 May 2015 (has links)
Neurostimulation continues to demonstrate tremendous success as an intervention for neurodegenerative diseases, including Parkinson's disease, in addition to a range of other neurological and psychiatric disorders. In an effort to enhance the medical efficacy and comprehension of this form of brain therapy, modeling and computational simulation are regarded as valuable tools that enable in silico experiments for a range of neurostimulation research endeavours. To fully realize the capacities of neurostimulation simulations, several areas within computation and numerics need to be considered and addressed. Specifically, simulations of neurostimulation that incorporate (i) computational efficiency, (ii) application versatility, and (iii) characterizations of cellularlevel electrophysiology would be highly propitious in supporting advancements in this medical treatment.
The focus of this dissertation is on these specific areas. First, preconditioners and iterative methods for solving the linear system of equations resulting from finite element discretizations of partial differential equation based transcranial electrical stimulation models are compared. Second, a software framework designed to efficiently support the range of clinical, biomedical, and numerical simulations utilized within the neurostimulation community is presented. Third, a multiscale model that couples transcranial direct current stimulation administrations to neuronal transmembrane voltage depolarization is presented. Fourth, numerical solvers for solving ordinary differential equation based ligandgated neurotransmitter receptor models are analyzed.
A fundamental objective of this research has been to accurately emulate the unique medical characteristics of neurostimulation treatments, with minimal simplification, thereby providing optimal utility to the scientific research and medical communities. To accomplish this, numerical simulations incorporate highresolution, MRIderived threedimensional head models, realworld electrode configurations and stimulation parameters, physiologicallybased inhomogeneous and anisotropic tissue conductivities, and mathematical models accepted by the brain modeling community. It is my hope that this work facilitates advancements in neurostimulation simulation capabilities, and ultimately helps improve the understanding and treatment of brain disease. / Ph. D.

5 
Aspects of finite volume method for compressible flowsKolibal, Joseph January 1989 (has links)
No description available.

6 
Assessing implicit large eddy simulation for twodimensional flowKent, James January 2009 (has links)
Implicit large eddy simulation (ILES) has been shown, in the literature, to have some success for threedimensional flow (e.g. see [Grinstein, F.F., Margolin, L.G. and Rider, W. Implicit Large Eddy Simulation. Cambridge, 2007]), but it has not previously been examined for twodimensional flow. This thesis investigates whether ILES can be applied successfully to twodimensional flow. Modified equation analysis is used to demonstrate the similarities between the truncation errors of certain numerical schemes and the subgrid terms of the barotropic vorticity equation (BVE). This presents a theoretical motivation for the numerical testing. Burgers equation is first used as a model problem to develop the ideas and methodology. Numerical schemes that are known to model Burgers equation well (shock capturing schemes) are shown to be implicitly capturing the subgrid terms of the onedimensional inviscid Burgers equation through their truncation errors. Numerical tests are performed on three equation sets (BVE, Euler equations and the quasigeostrophic potential vorticity equation) to assess the application of ILES to twodimensional flow. The results for each of these equation sets show that the schemes considered for ILES are able to capture some of the subgrid terms through their truncation errors. In terms of accuracy, the ILES schemes are comparable (or outperform) schemes with simple explicit subgrid models when comparing vorticity solutions with a high resolution reference vorticity solution. The results suggest that conservation of vorticity is important to the successful application of ILES to twodimensional flow, whereas conservation of momentum is not. The schemes considered for ILES are able to successfully model the downscale enstrophy transfer, but none of the schemes considered for ILES (or the schemes with simple subgrid models) can model the correct upscale energy transfer from the subgrid to the resolved scales. Energy backscatter models are considered and are used with the ILES schemes. It is shown that it is possible to create an energy conserving and enstrophy dissipating scheme, composed of an ILES scheme and a backscatter model, that improves the accuracy of the vorticity solution (when compared with the corresponding ILES scheme without backscatter).

7 
Search for Perfect Complementary Codes Using Nonlinear Numerical MethodsTsai, shianming 02 September 2005 (has links)
This paper present three kinds of nonlinear numerical methods to search for perfect complementary codes, include Newtonian Methods¡BLevenbergMarquardt Algorithm and TrustRegions. By searching for the solution of theses nonlinear equations, we can get complementary codes when setting for the length of element codes and the flock size. These search results is very generous. Complete complementary codes¡Bsuper complementary code and polyphase complementary code are subsets of these searching results¡C
These nonlinear equations are set to have ideal autocorrelation and crosscorrelation properties, so the searching results of these nonlinear equations are still have perfect orthogonal complementary properties.
Because the orthogonal complementary code is obtained via these nonlinear equations, the results are the most generous. So nonlinear numerical method is a good choice to search for another complementary code we don¡¦t know.

8 
Research of valuation and numerical methods of pathdependent optionsLin, MingYing 31 July 2001 (has links)
none

9 
Skaitiniai metodai kompiuterinės matematikos sistemose / Numerical methods in computer algebra systemsProkopovič, Jelena 13 June 2005 (has links)
In this work there are analized the realization of the most important numerical methods in computer algebra systems. There are analyzed and comparised the opportiunities of three CAS – Maple, Matlab and Mathcad – for the reason how to solve the mathematical tasks by using the numerical methods. Therefore are given the discription of the methods for solving systems of linear equations, function interpolation, numerical integration and for solving the first order differential equations. There is analyzed how those methods are realized in the CAS. In the last unit the numerical methods of those systems are compared by their complication, convinience for the user and the variety of functions of the numerical methods. After the description of every method there are proposed the examples of the task solutions by using CAS.

10 
Numerical solution of a freeboundary viscous flowShola, Peter Bamidele January 1990 (has links)
No description available.

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