Meshless and Multi-Resolution Collocation Techniques for Steady State Interface Models

DOI10.1142/S0219876217500736zbMath1404.65067MaRDI QIDQ4563098

Imran Aziz, Nadeem Haider, Siraj-ul-islam

Publication date: 6 June 2018

Published in: International Journal of Computational Methods (Search for Journal in Brave)

zbMATH Keywords

radial basis functionsHaar waveletmeshless methodelliptic modelsdouble interface conditionssingle interface conditions

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

An Efficient Numerical Scheme for the Solution of a Stochastic Volatility Model Including Contemporaneous Jumps in Finance ⋮ A reliable and fast mesh-free solver for the telegraph equation ⋮ Local radial basis function collocation method for Stokes equations with interface conditions ⋮ Meshless and multi-resolution collocation techniques for parabolic interface models

Uses Software

• IIMPACK

Cites Work

• Unnamed Item
• A matched interface and boundary method for solving multi-flow Navier-Stokes equations with applications to geodynamics
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• The numerical solution of second-order boundary-value problems by collocation method with the Haar wavelets
• Numerical solution of evolution equations by the Haar wavelet method
• Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
• Meshfree explicit local radial basis function collocation method for diffusion problems
• Convergence order estimates of meshless collocation methods using radial basis functions
• Numerical analysis of blood flow in the heart
• An efficient numerical scheme for Burger equation
• A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
• Haar wavelet approach to linear stiff systems.
• A comparative analysis of local meshless formulation for multi-asset option models
• Numerical solution of differential equations using Haar wavelets
• A boundary condition capturing method for Poisson's equation on irregular domains
• High-order difference potentials methods for 1D elliptic type models
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• Simplified immersed interface methods for elliptic interface problems with straight interfaces
• The immersed boundary method
• Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Convergence of the ghost fluid method for elliptic equations with interfaces
• Estimation of Dispersion in an Open Channel from an Elevated Source Using an Upwind Local Meshless Method
• High Order Unfitted Finite Element Methods for Interface Problems and PDEs on Surfaces
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver
• The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions
• The Immersed Interface Method
• Haar wavelet approach to nonlinear stiff systems
• Discontinuous Galerkin immersed finite element methods for parabolic interface problems