Semi-implicit methods for advection equations with explicit forms of numerical solution

Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations

We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition methods, which, when compared with Schwarz-algorithm-based parabolic solvers, are computationally and communicationally efficient for each sim...

Inflow-Implicit/Outflow-Explicit Scheme for Solving Advection Equations

We present new method for solving non-stationary advection equations based on the finite volume space discretization and the semi-implicit discretization in time. Its basic idea is that outflow from a cell is treated explicitly while inflow is treated implicitly. Since the matrix of the system in this new I2OE method is determined by the inflow fluxes it is an M-matrix yielding favourable solva...

Numerical Solution of Advection-Diffusion-Reaction Equations

Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations

We introduce a new class of methods for solving non-stationary advection equations. The new methods are based on finite volume space discretizations and a semi-implicit discretization in time. Its basic idea is that outflow from a cell is treated explicitly while inflow is treated implicitly. This is natural, since we know what is outflowing from a cell at the old time step but we leave the met...

Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated i...