Papers by Yin-Liang Huang
Contemporary mathematics, 2005
We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is ... more We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.
Communications in Computational Physics, Mar 1, 2011
We present a fast Poisson solver on spherical shells. With a special change of variable, the radi... more We present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with O(N 3 log N) operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.
Contemporary Mathematics, 2005
We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is ... more We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.
Communications in Computational Physics, 2011
We present a fast Poisson solver on spherical shells. With a special change of variable, the radi... more We present a fast Poisson solver on spherical shells. With a special change of variable, the radial part of the Laplacian transforms to a constant coefficient differential operator. As a result, the Fast Fourier Transform can be applied to solve the Poisson equation with operations. Numerical examples have confirmed the accuracy and robustness of the new scheme.
SIAM Journal on Scientific Computing, 2015
We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalue... more We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of the degenerate elliptic operator arising from Maxwell's equations. We consider spatial compatible discretizations such as Yee's scheme which guarantee the existence of a discrete vector potential. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential instead. The correction equation is solved approximately as in original Jacobi-Davidson approach. The computational cost of the transformation from the vector potential to the corrector is negligible. As a consequence, the expanding subspace automatically stays out of the null space and no extra projection step is needed. Numerical evidence confirms that the new method is much more efficient than the original Jacobi-Davidson method.
SIAM Journal on Scientific Computing, 2013
We propose a simple finite difference scheme for Navier-Stokes equations in primitive formulation... more We propose a simple finite difference scheme for Navier-Stokes equations in primitive formulation on curvilinear domains. With proper boundary treatment and interplay between covariant and contravariant components, the spatial discretization admits exact Hodge decomposition and energy identity. As a result, the pressure can be decoupled from the momentum equation with explicit time stepping. No artificial pressure boundary condition is needed. In addition, it can be shown that this spatially compatible discretization leads to uniform inf-sup condition, which plays a crucial role in the pressure approximation of both dynamic and steady state calculations. Numerical experiments demonstrate the robustness and efficiency of our scheme.
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Papers by Yin-Liang Huang