Parallel Implementation of the Matrix Formulation of the FDTD Scheme

2007 ◽  
Author(s):  
Piotr Sypek ◽  
Michal Wiktor ◽  
Michal Mrozowski
Keyword(s):  
Parallel Implementation ◽  
Matrix Formulation ◽  
The Matrix

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

Multiply Separated Synthesis of Six-Link Mechanisms Using Parallel Homotopy With M-Homogenization

1998 ◽  
Author(s):  
A. K. Dhingra ◽  
M. Zhang
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Parallel Implementation ◽  
Homotopy Methods ◽  
Numerical Work ◽  
Function Generation ◽  
Connection Machine ◽  
The Matrix ◽  
Generation Problem ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function generation problem of six-link Watt and Stephenson mechanisms, with multiply separated precision positions (PP), using homotopy methods with m-homogenization. It is seen that using the matrix method for synthesis, applying m-homogeneous group theory and by defining auxiliary equations in addition to the synthesis equations, the number of homotopy paths to be tracked in obtaining all possible solutions to the synthesis problem can be drastically reduced. Numerical work dealing with the synthesis of Watt and Stephenson mechanisms for 6 and 9 multiply separated precision points is presented. For both mechanisms, it is seen that complete solutions for 6 and 9 precision points can be obtained by tracking 640 and 286,720 paths, respectively. A parallel implementation of homotopy methods on the Connection Machine on which several thousand homotopy paths can be tracked concurrently is also discussed.

scholarly journals The matrix formulation of type IIB five-branes

1998 ◽  
Vol 523 (1-2) ◽  
pp. 158-170 ◽  
Author(s):  
Savdeep Sethi
Keyword(s):  
Matrix Formulation ◽  
The Matrix

Closed Shell Hartree Theory with Orthonormal Orbitals

1980 ◽  
Vol 35 (4) ◽  
pp. 408-411 ◽  
Author(s):  
Yasuyuki Ishikawa
Keyword(s):  
Closed Shell ◽  
Natural Orbital ◽  
Matrix Formulation ◽  
The Matrix ◽  
Polyatomic Systems

Abstract A natural orbital multiconfigurational SCF formalism has been applied to the closed shell Hartree theory with orthonormal orbitals. A prescription is given for constructing a single, one-electron Hamiltonian with which one can determine all the occupied orbitals. The formalism is suited to the matrix formulation of the orthogonalized Hartree theory for polyatomic systems.

scholarly journals Comparison of Three Recent Personalization Algorithms

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Matrix Factorization ◽  
Parallel Implementation ◽  
Apache Spark ◽  
Test Set ◽  
Hit Rate ◽  
The Matrix ◽  
Bayesian Personalized Ranking ◽  
Personalized Ranking

<p>Personalization algorithms recommend products to users based on their previous interactions with the system. The products could be books, movies, or products in a retail system. The earliest personalization algorithms were based on factorization of the user-item matrix where each entry in the matrix would correspond to an interaction, or absence of an interaction of the user with the product. In this article, we compare three recently developed personalization algorithms. The three algorithms are Bayesian Personalized Ranking, Taxonomy Discovery for Personalized Recommendations and Multi-Matrix Factorization. We compare the three algorithms on the hit rate @ position 10 on a held out test set on 1 million users and 200 thousand items in the catalog of Target Corporation. We report our findings in table 1. We develop all three algorithms on an Apache Spark parallel implementation.</p>

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