In this paper we present a family of scalable preconditioners for matrices arising in the discretization of H(div) problems using the lowest order Raviart-Thomas finite elements. Our approach belongs to the class of “auxiliary space”-based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of m...

We use the Lin-Maldacena prescription to demonstrate how to find the supergravity solutions dual to arbitrary vacua of the plane wave matrix model and maximally supersymmetric Yang-Mills theory on R × S2, by solving the auxiliary electrostatics problem. We then apply the technique to study instantons at strong coupling in the matrix model.

The purpose of the paper is to introduce a new type of fuzzy matrix games: fuzzy constrained matrix games. A computational method for its solution based on establishment of the auxiliary fuzzy linear programming for each player is proposed. The approach based on the multiobjective programming is established to solve these fuzzy linear programming. Effectiveness is illustrated with a numerical e...

The spectra of recently constructed auxiliary matrices for the six-vertex model respectively the spin s = 1/2 Heisenberg chain at roots of unity are investigated. Two conjectures are formulated both of which are proven for N = 3 and are verified numerically for several examples with N > 3. The first conjecture identifies an abelian subset of auxiliary matrices whose eigenvalues are polynomials ...

We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This happens at the saddle point for the Yang-Mills field. It turns out that the large-n limit in this matrix model corresponds to a double scaling limit in the P...

data type, 151, 184Ackermann function, 103, 105, 115Ada, 32, 51add, 56adjacency-list representation, 69adjacency-matrix representation, 69aggregate expression, 50, 57Aho, 21ALGOL, 51alias,153, 160, 165, 204alias analysis, 160, 204, 211all, 57Allen, 20, 51Alloy, 21Analytical Engine, 32, 51anchor of auxiliary map, 126Andersen, 14...

Two different forms of a preconditioning process (i.e. standard preconditioning and quasi-diagonalization) are presented, in conjunction with the Method of Auxiliary Sources (MAS), when the latter is applied to a specific class of two-dimensional scattering problems. The method enhances the efficiency of MAS, when the linear system becomes illconditioned, due to distancing of the auxiliary surf...