Journal of Computational Physics
On finite element domain imbedding methods
SIAM Journal on Numerical Analysis
Preconditioning capacitance matrix problems in domain imbedding
SIAM Journal on Scientific Computing
A spectral embedding method applied to the advection-diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Spectral methods in MATLAB
On a Boundary Control Approach to Domain Embedding Methods
SIAM Journal on Control and Optimization
SIAM Journal on Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
Computers & Mathematics with Applications
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
Computational Mechanics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Hi-index | 7.30 |
Spectral methods are a class of methods for solving partial differential equations (PDEs). When the solution of the PDE is analytic, it is known that the spectral solutions converge exponentially as a function of the number of modes used. The basic spectral method works only for regular domains such as rectangles or disks. Domain decomposition methods/spectral element methods extend the applicability of spectral methods to more complex geometries. An alternative is to embed the irregular domain into a regular one. This paper uses the spectral method with domain embedding to solve PDEs on complex geometry. The running time of the new algorithm has the same order as that for the usual spectral collocation method for PDEs on regular geometry. The algorithm is extremely simple and can handle Dirichlet, Neumann boundary conditions as well as nonlinear equations.