Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for mimetic discretizations using algebraic topology to guide our analysis. The framework and all attendant discrete structures are put together by using two basic mappings between differential forms and co...

In this paper, we present an adaptive approach to design the artificial boundary conditions for the two-level Schrödinger equation with conical crossings on the unbounded domain. We use the windowed Fourier transform to obtain the local wave number information in the vicinity of artificial boundaries, and adopt the operator splitting method to obtain an adaptive local artificial boundary condit...

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A support operators (operator-difference) method has proven itself well for implicit simulations of different astrophysical fluid flows. Following the operator-difference approach, we construct nodal difference analogues differential in Cartesian coordinates, where conjugacy properties are same as original ones. Using operators, develop an Eulerian semi-implicit gas-dynamical solver with self-g...