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Full-Text Articles in Engineering
A Fast Adaptive Wavelet Scheme In Rbf Collocation For Nearly Singular Potential Pdes, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Shekarchi, Mohammad Rahimian
A Fast Adaptive Wavelet Scheme In Rbf Collocation For Nearly Singular Potential Pdes, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Shekarchi, Mohammad Rahimian
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
We present a wavelet based adaptive scheme and investigate the efficiency of this scheme for solving nearly singular potential PDEs. Multiresolution wavelet analysis (MRWA) provides a firm mathematical foundation by projecting the solution of PDE onto a nested sequence of approximation spaces. The wavelet coefficients then were used as an estimation of the sensible regions for node adaptation. The proposed adaptation scheme requires negligible calculation time due to the existence of the fast DiscreteWavelet Transform (DWT). Certain aspects of the proposed adaptive scheme are discussed through numerical examples. It has been shown that the proposed adaptive scheme can detect the …
Stable Pde Solution Methods For Large Multiquadric Shape Parameters, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
Stable Pde Solution Methods For Large Multiquadric Shape Parameters, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination.
A Stabilized Rbf Collocation Scheme For Neumann Type Boundary Value Problems, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
A Stabilized Rbf Collocation Scheme For Neumann Type Boundary Value Problems, Nicolas Ali Libre, Arezoo Emdadi, Edward J. Kansa, Mohammad Rahimian, Mohammad Shekarchi
Civil, Architectural and Environmental Engineering Faculty Research & Creative Works
The numerical solution of partial differential equations (PDEs) with Neumann boundary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neumann BC requires the approximation of the spatial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. Increased accuracy of the spatial derivative approximation can be achieved by h-refmement reducing the …