An FC-based spectral solver for elastodynamic problems in general three-dimensional domains

A spectral FC solver for the compressible Navier-Stokes equations in general domains I: Explicit time-stepping

We present a Fourier continuation (FC) algorithm for the solution of the fully nonlinear compressible Navier–Stokes equations in general spatial domains. The new scheme is based on the recently introduced accelerated FC method, which enables use of highly accurate Fourier expansions as the main building block of general-domain PDE solvers. Previous FC-based PDE solvers are restricted to linear ...

Efficient and accurate three-dimensional Poisson solver for surface problems.

We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are needed for all kinds of surface problems. Our method has an O(N log N) computational cost, where N is the number of grid points, with a very small prefactor. Thi...

h-p Spectral element methods for three dimensional elliptic problems on non-smooth domains

1Department of Mathematics & Statistics, Indian Institute of Technology, Kanpur 208 016, India 2Department of Mathematics, The LNM Institute of Information Technology, Jaipur 302 031, India 3TIFR Centre For Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560 065, India 4Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India *Correspo...

A General Boundary-Integral Formulation for Zoned Three-Dimensional Media

A new boundary-integral formulation is proposed to analyze the heat transfer in zoned three-dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula, and the exterior formula. An advantage of this formulation over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formul...

A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems