Abstract The numerical approach for solving the fixed gravimetric boundary value problem (FGBVP) based on finite element method (FEM) with mapped infinite elements is developed and implemented. In this approach, 3D semi-infinite domain outside Earth bounded by triangular discretization of whole Earth’s surface extends to infinity. Then FGBVP consists Laplace equation unknown disturbing potentia...

We are developing a new class of finite-volume methods on locally-refined and mapped grids, which are at least fourth-order accurate in regions where the solution is smooth. This paper discusses the implementation of such methods for time-dependent problems on both Cartesian and mapped grids with adaptive mesh refinement. We show 2D results with the Berger–Colella shock-ramp problem in Cartesia...

1 2 , γ γ , can be mapped conveniently onto a matrix. The expectation value of the this operator <Ψ|H|Ψ > will lead to a corresponding eigenpair. We can map the gird of H using a simple finite difference equation, onto a vector whose elements are defined as, {Ψ00, Ψ10, ..., Ψn0, Ψn1, ..., Ψnn}. When the corresponding eigenvector is found, these elements are then mapped back onto their correspon...

We study the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits. On input of a finite set of variables and a finite set of constraints the question is whether the variables can be mapped onto finite subsets of N (resp., finite intervals over N) such that all constraints are satisfied. According to the operations allowed in t...