Solving boundary value problems via the Nyström method using spline Gauss rules

Numerical computation using splines (65D07) Numerical methods for integral equations (65R20) Numerical quadrature and cubature formulas (65D32) Fredholm integral equations (45B05) Boundary element methods for boundary value problems involving PDEs (65N38)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
A simplified technique for the efficient and highly accurate discretization of boundary integral equations in 2D on domains with corners
High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane
On the solution of Fredholm integral equations based on spline quasi-interpolating projectors
Solving Fredholm integral equations by approximating kernels by spline quasi-interpolants
Efficient quadrature for NURBS-based isogeometric analysis
Isogemetric analysis and symmetric Galerkin BEM: a 2D numerical study
Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme
Gaussian quadrature for splines via homotopy continuation: rules for $C^2$ cubic splines
A Nyström method for boundary integral equations in domains with corners
Error analysis for a class of degenerate kernel methods
A new approach to the numerical solution of integral equations
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nyström discretization
Two methods based on bivariate spline quasi-interpolants for solving Fredholm integral equations
Integral equations. Theory and numerical treatment
Shape optimization of conductive-media interfaces using an IGA-BEM solver
A quasi-interpolation product integration based method for solving Love's integral equation with a very small parameter
A Nyström-based finite element method on polygonal elements
On the application of isogeometric finite volume method in numerical analysis of wet-steam flow through turbine cascades
Stochastic isogeometric analysis method for plate structures with random uncertainty
A discrete collocation scheme to solve Fredholm integral equations of the second kind in high dimensions using radial kernels
Superconvergent methods based on quasi-interpolating operators for Fredholm integral equations of the second kind.
The isogeometric Nyström method
Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
The isogeometric boundary element method
An efficient high-order Nyström scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface
Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
Spline quasi-interpolating projectors for the solution of nonlinear integral equations
Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors
An accurate integral equation method for Stokes flow with piecewise smooth boundaries
On numerical solution of Fredholm and Hammerstein integral equations via Nyström method and Gaussian quadrature rules for splines
Multistep collocation method for Fredholm integral equations of the second kind
Refined isogeometric analysis of quadratic eigenvalue problems
Hierarchical enrichment for bridging scales and mesh-free boundary conditions
Imposing Dirichlet boundary conditions with Nitsche's method and spline-based finite elements
Spline functions, convex curves and mechanical quadrature
Theoretical Numerical Analysis
Discrete Collocation Methods for Second Kind Fredholm Integral Equations
Discrete Galerkin Methods for Fredholm Integral Equations of the Second Kind
The Discrete Galerkin Method for Integral Equations
Moment Theory for Weak Chebyshev Systems with Applications to Monosplines, Quadrature Formulae and Best One-Sided $L^1 $-Approximation by Spline Functions with Fixed Knots
A Collocation Method for Fredholm Integral Equations of the Second Kind
An analysis of the coupling of finite-element and Nyström methods in acoustic scattering
The Numerical Solution of Integral Equations of the Second Kind
Isogeometric Analysis
Locally Corrected Multidimensional Quadrature Rules for Singular Functions
Non-uniform quasi-interpolation for solving Hammerstein integral equations
Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems
The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
Numerical Analysis
Linear integral equations

This page was built for publication: Solving boundary value problems via the Nyström method using spline Gauss rules