We construct and analyze first- second-order implicit-explicit schemes based on the scalar auxiliary variable approach for magneto-hydrodynamic equations. These are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, unconditionally energy stable. derive rigorous error estimates velocity, pressure, magnetic field first-order sch...

A partitioning problem on chordal graphs that arises in the solution of sparse triangular systems of equations on parallel computers is considered Roughly the problem is to partition a chordal graph G into the fewest transitively orientable subgraphs over all perfect elimination orderings of G subject to a certain precedence relationship on its vertices In earlier work a greedy scheme that solv...

A finite-volume model has been developed to study incompressible forced flow heat transfer of air over a circular cylinder in cross flow. An artificial compressibility technique is applied to couple the continuity to the momentum equations. The proposed explicit finite-volume method (FVM) uses a novel discretization in time and space. The governing equations are solved by time-marching using a ...

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step. This decomposition is obtained through the use of an efficient modified Progressive Generalized Decomposition (PGD) method, whose convergence is proved. We sug...

A numerical scheme for solving the time evolution of wave functions under the time-dependent Kohn-Sham (TDKS) equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time step for solving the time evolution...

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain-Antichain Principle (CAC). Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC ` WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a wel...

The dynamic assembly of microtubules is a key factor in many of their functions in the cell and recent experiments give new insight into this process at the molecular level.