Spectral collocation and radial basis function methods for one-dimensional interface problems
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The random feature method for solving interface problems
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2022, Engineering Analysis with Boundary ElementsA generalized finite difference method for solving elliptic interface problems
2020, Mathematics and Computers in SimulationLocal meshless methods for second order elliptic interface problems with sharp corners
2020, Journal of Computational PhysicsCitation Excerpt :Unlike the conventional methods, meshless methods can cope with scattered data and irregular geometries should the need arise. Meshless methods based on differential quadrature [23] (also known as RBF-FD methods) with global integrated RBFs and ordinary RBFs have recently been used in [24–27] for numerical solution of steady and unsteady interface PDEs in irregular domain settings (see also [28]). In the construction of strong form meshless approximations, RBFs can be used both globally and locally.
Least squares spectral method for the two-dimensional Stokes interface problems
2020, Journal of Computational and Applied MathematicsCitation Excerpt :In addition, the algebraic system which must be solved to compute the discrete solution is always symmetric and positive definite and can be easily preconditioned. The pseudo-spectral method for one dimensional interface problems has been developed in [11]. Hessari et al. [12] have developed an algorithm to approximate the solutions of second order elliptic interface problems using pseudo-spectral element method.
Meshless analysis of parabolic interface problems
2018, Engineering Analysis with Boundary ElementsCitation Excerpt :The RBFs that have been integrated several times appeared to be superior to the standard non-integrated RBFs, when the function being approximated is sufficiently smooth. Numerical solutions of various interface parabolic and elliptic PDEs related to mathematical modeling of diffusion-transport related processes [25–32], are challenges ridden. Such type of PDEs have wide ranging applications in science and engineering.