In this paper, we present the mathematical analysis of a covolume method for the approximations of the Ginzburg–Landau (GL) model for superconductivity. A nice feature of this approach is that the gauge invariance properties are retained in discrete approximations based on triangular grids. We also use properties of discrete vector fields to study issues such as the gauge choices and their enfo...

The offset surfaces to non-developable quadratic triangular Bézier patches are rational surfaces. In this paper we give a direct proof of this result and formulate an algorithm for computing the parameterization of the offsets. Based on the observation that quadratic triangular patches are capable of producing C smooth surfaces, we use this algorithm to generate rational approximations to offse...

Equilibrium Wulff shapes and interfacial energies of two-dimensional ‘‘crystals’’ on a triangular lattice are considered. Asymptotic approximations are constructed for both the shapes and energies in the limit T→0 where crystals are close to perfect hexagons, and the limit T→Tc ~critical temperature! where crystals have near-circular shapes. The intermediate temperature region is studied numeri...

In the second part of this two-part paper, we derive approximations to the signal-to-interference plus noise power ratio (SINR) attainable by PCC, SCC, and windowing and compare their performances in terms of SINR. We also derive an asymptotically optimal window and discuss the optimality of the triangular window for ICI reduction. Finally, we derive approximations to bit-errorrate (BER) attain...

A proximity matrix, morse digits.dat, for the ten Morse code symbols representing the first ten digits (data from Rothkopf, 1957). 33 9.1 Order-constrained least-squares approximations to the digit proximity data of Shepard et al. (1975); the upper-triangular portion is anti-Robinson and the lower-triangular portion is strongly-anti-The 45 subsets listed according to increasing diameter values ...

Topologically consistent algorithms for the intersection and trimming of free-form parametric surfaces are of fundamental importance in computer-aided design, analysis, and manufacturing. Since the intersection of (for example) two bicubic tensor-product surface patches is not a rational curve, it is usually described by approximations in the parameter domain of each surface. If these approxima...

BLOCK TRIANGULAR PRECONDITIONERS FOR -MATRICES AND MARKOV CHAINS MICHELE BENZI AND BORA UÇAR Abstract. We consider preconditioned Krylov subspace methods for solving large sparse linear systems under the assumption that the coefficient matrix is a (possibly singular) -matrix. The matrices are partitioned into block form using graph partitioning. Approximations to the Schur complement are used t...

Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem. In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem. In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs. We compare a greedy heuristic against a triangular cactus he...

Discrete approximations to hyperbolic partial differential equations governing frictionless two-dimensional fluid flow are developed in Cartesian geometry for use over arbitrary triangular grids. A class of schemes is developed that conserves mass, momentum, and total energy. The terms of the governing equations are also approximated individually and their truncation error is examined. For test...