A direct method of lines and a numerical algorithm are proposed for solving Poisson's equation in a nonrectangular domain with the Dirichlet boundary condition. They are based on the method of lines, a fictitious domain and a distribution theoretical formulation.
This paper proposes a new estimation method of the renewal function from i. i. d. observations of the inter-arrival time, using a radial basis function (RBF) type of neural network. The basic idea is to solve numerically the discritized renewal equation based on the corresponding empirical distribution function to the observations. The RBF neural network is applied to approximate the underlying empirical distribution. Throughout numerical experiments, we show that the proposed method can estimate the renewal function with higher precision than existing statistical methods for a pattern data.
We developed a noble algorithm for large-scale Fock matrix generation with small local distributed memory architecture. We call it "RT parallel algorithm". The outer loop is index RT, which is determined by the combination of contracted shell indexes R and T. Indexes of inner S and U loop are determined by RS cutoff and TU cutoff. The RT parallel algorithm needs O(N) amounts of communication between a host computer and parallel processors per O(N^2) integral calculations and indexes of communicated matrix elements are also determined by the cutoff operation. Therefore we can conceal the communication time behind the calculation time. The memory amounts of processor elements do not depend on the number of basis sets since the number of cutoff-survived indexes is saturated in large-scale molecules. So we can say that the RT parallel algorithm is scalable. The RT parallel algorithm has considered the partial summing technigue which is indispensable for computing accuracy, and it can adopt another Fock matrix calculation method using the change in density matrix and therefore, the RT parallel algorithm can realize the large-scale Fock matrix calculation with small local distributed memories.
In this paper we describe the morphological operator present which generate artistic calligraphy characters with scratched look or blurred look. This operator generates artistic characters from the original calligraphy fonts which are True Type, Bitmap, and so on. The operator consists of dilations and erosions, which are which are fundamental operation of mathematical morphology. This method makes it possible that a computer gives users various scratched or blurred look calligraphic characters without increasing amount of prepared data of calligraphic characters.
This paper uses a generalization of the SMAC method, which is commonly used to solve incompressible Navier-Stokes equations, to demonstrate that a simultaneous velocity-pressure relaxation algorithm for the HSMAC method is equivalent to a SOR algorithm for a discretized pressure Poisson equation. Two computational algorithms are introduced, each of which uses the conjugate gradient (CG) method for the solution of the pressure Poisson equation. The first uses a simultaneous velocity-pressure relaxation-type CG method ; the second uses a CG method without matrix representation.