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Showing 1 to 14 of 14 for “"fundamental solutions"”.
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Spectral approach for improving the Ill-conditioning of the method of fundamental solutions
… das soluções fundamentais, em inglês, method of fundamental solutions (MFS), é um método para solução de problemas de valor de fronteira de equações diferenciais com derivadas parciais. O método pertence à classe dos métodos que não necessitam de discretização do domínio, evitando, dessa forma, …
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A Comparison of Two Boundary Methods For Biharmonic Boundary Value Problems
… The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS …
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Conformally Invariant Operators in Higher Spin Spaces
… we generalize these operators and their fundamental solutions to some conformally flat manifolds, such as cylinders and Hopf manifolds. To generalize our results to the case where the target space is a degree k homogeneous polynomial space, we first construct third order and fourth order …
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A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations
… with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary …
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Fractional Diffusion in Gaussian Noisy Environment
… We prove the existence and uniqueness of the solutions and obtain some properties of the solutions. Chapter 3 studies the linear stochastic partial differential equation of fractional orders both in time and space variables. We prove the existence and uniqueness of the solution and calculate …
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Numerical solutions to Poisson's equation using radial basis functions
This thesis addresses the problem of obtaining solutions to Poisson's equation which is encountered in the applied sciences and engineering fields. Two separate methods are explained for obtaining particular solutions to this equation. The Method of Fundamental Solutions is then used to solve the …
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Distribuição de pontos fonte para o método das soluções fundamentais: aplicação a problemas de ondas acústicas em domínios exteriores em R3
… das soluções fundamentais (MFS - method of fundamental solutions) que otimize o condici-onamento do sistema linear associado à resolução numérica do problema exterior de difração de um campo acústico incidente por um obstáculo tridimensional impenetrável conhecido (𝐷). Considera-se que o …
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Development and applications of hypersingular boundary integral equations for three-dimensional acoustics and elastodynamics
… this purpose, three integral identities for the fundamental solutions of both potential and elastostatic problems are established and employed. These weakly-singular forms of the hypersingular BIE's can be handled easily and no special quadratures are needed in the numerical computation. The …
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On intrinsic ultracontractivity of perturbed Levy processes and applications of Levy processes in actuarial mathematics
… values analytically, which leads to efficient solutions to its pricing problem. In the second part, we consider the intrinsic ultracontractivity of certain Levy processes under nonlocal perturbations. More precisely, we establish the intrinsic ultracontractivity of the Laplacian (corresponding …
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Novel Bioinspired Pumping Models for Microscale Flow Transport
… numerical method is based on the method of fundamental solutions (MFS) that uses a set of singularized force elements ``Stokeslets'' to induce the flow motions. Moreover, the passive particle tracking simulation approach in the Lagrangian frame of reference is also used to strengthen and …
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Physically Based Mesh-free Deformation Framework and Techniques for Computer Graphics
… and a deformation is defined as a combination of fundamental solutions. Because no mesh is involved, deforming a complex shape is as straightforw'ard as deforming a simple one and the trade-off between efficiency and accuracy is easy to achieve by redistributing the points concerned. Experiments …
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A Boundary Element Method for Thermo-poroelasticity with Applications in Rock Mechanics
… and DD methods. The boundary integral equations, fundamental solutions, and the numerical implementations for the development of this model are described. The model is tested using some poroelastic and thermo-poroelastic examples. The numerical predictions show good agreement with analytical …
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Three-dimensional layerwise modeling of layered media with boundary integral equations
… Explicit expressions are obtained for the fundamental solution of the typical infinite layer, which are applied in the two-dimensional boundary integral equation model to produce the integral representation of the solution. The boundary integral equation model is two-dimensional, …
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Design, Fabrication and Modelling of Intracardiac Catheter for Electrical Mapping of Atrial Fibrillation
… A novel in-silico test bed using the method of fundamental solutions (MFS) approach was used to test various MBC designs in inverse mapping. This is novel in a way that it provided a more realistic representation of the physiological makeup of atria accounting for the presence of inlet and …