Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A spectral embedding method applied to the advection-diffusion equation
Journal of Computational Physics
On the Gibbs Phenomenon and Its Resolution
SIAM Review
Stokes flow in a channel obstructed by a row of cylinders
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
A Fat Boundary Method for the Poisson Problem in a Domain with Holes
Journal of Scientific Computing
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
Journal of Computational Physics
Spectral distributed Lagrange multiplier method: algorithm and benchmark tests
Journal of Computational Physics
SIAM Journal on Scientific Computing
A direct-forcing fictitious domain method for particulate flows
Journal of Computational Physics
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Journal of Computational Physics
Journal of Computational Physics
Spectral domain embedding for elliptic PDEs in complex domains
Journal of Computational and Applied Mathematics
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
Journal of Computational Physics
On the resolution power of Fourier extensions for oscillatory functions
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multipliers and the novel aspect is that the Lagrange multipliers are associated with smooth forcing functions, compactly supported inside the fictitious domain. This allows the accuracy of the spectral method to be preserved, unlike the classical discrete Lagrange multipliers method, in which the forcing is defined on the boundaries. In order to have a robust and efficient method, equations for the Lagrange multipliers are solved directly with an influence matrix technique. Using a Fourier-Chebyshev approximation, the high-order accuracy of the method is demonstrated on one- and two-dimensional elliptic problems of second- and fourth-order. The principle of the method is general and can be applied to solve elliptic problems using any high order variational approximation.