scholarly journals Discrete Gaussian Leftover Hash Lemma over Infinite Domains

2013 ◽  
pp. 97-116 ◽  
Author(s):  
Shweta Agrawal ◽  
Craig Gentry ◽  
Shai Halevi ◽  
Amit Sahai
Keyword(s):  
Infinite Domains

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Preface

2011 ◽  
Vol 21 (4) ◽  
pp. 671-677 ◽  
Author(s):  
GÉRARD HUET
Keyword(s):  
Mathematical Logic ◽  
Computer Science ◽  
20Th Century ◽  
Theorem Proving ◽  
Propositional Calculus ◽  
Interactive Theorem Proving ◽  
Predicate Calculus ◽  
Special Issue ◽  
Mathematical Structures ◽  
Infinite Domains

This special issue of Mathematical Structures in Computer Science is devoted to the theme of ‘Interactive theorem proving and the formalisation of mathematics’.The formalisation of mathematics started at the turn of the 20th century when mathematical logic emerged from the work of Frege and his contemporaries with the invention of the formal notation for mathematical statements called predicate calculus. This notation allowed the formulation of abstract general statements over possibly infinite domains in a uniform way, and thus went well beyond propositional calculus, which goes back to Aristotle and only allowed tautologies over unquantified statements.

Kelvin transformations for simulations on infinite domains

2021 ◽  
Vol 40 (4) ◽  
pp. 1-15
Author(s):  
Mohammad Sina Nabizadeh ◽  
Ravi Ramamoorthi ◽  
Albert Chern
Keyword(s):  
Infinite Domains

scholarly journals Time Domain Implementation of Transmitting Boundaries in ABAQUS for Discrete Soil-structure Interaction Systems

2020 ◽  
Vol 5 (3) ◽  
pp. 447-462
Author(s):  
J. Rama Raju Patchamatla ◽  
P. K. Emani
Keyword(s):  
Time Domain ◽  
Soil Structure ◽  
Seismic Waves ◽  
Seismic Analysis ◽  
Discrete Models ◽  
Soil Structure Interaction ◽  
Finite Domain ◽  
Infinite Domains ◽  
Structure Interaction ◽  
Transmitting Boundaries

Soil-structure-interaction (SSI) analyses are essential to evaluate the seismic performance of important structures before finalizing their structural design. SSI under seismic condition involves much more complex interaction with soil compared to the dynamic loads having source on the structure. Seismic SSI analysis requires due consideration of site-specific and structure-specific properties to estimate the actual ground motion (scattered motion) experienced at the base of the structure, and subsequently the effects of the scattered motion on the structure. Most challenging aspect of seismic SSI analysis is to implement transmitting boundaries that absorb the artificial reflections of stress waves at the truncated interface of the finite and infinite domains, while allowing the seismic waves to enter the finite domain. In this paper, the time domain implementation of seismic analysis of a soil-structure system is presented using classical discrete models of structure and interactive force boundary conditions for soil. These models represent typical SSI systems- a single Degree of Freedom (DOF) of a spherical cavity with mass attached to its wall, a two DOF system consisting of a mass attached by a nonlinear spring to a semi-infinite rod on elastic foundation, and a three DOF system with additional DOFs for modelling the structural stiffness and damping. The convolution integral representing the force boundary condition on the truncated interface, is evaluated interactively using UAMP user-subroutine in ABAQUS and applied as concentrated forces at the interface (truncated interface) nodes of the bounded domain or generalized-structure domain. The verification problems presented in the paper show the satisfactory performance of the developed MATLAB code and ABAQUS implementation with FORTRAN user-subroutines. The classical phenomena associated with the dynamic soil-structure systems are discussed through the present work.

The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary

1999 ◽  
Vol 6 (6) ◽  
pp. 517-524
Author(s):  
M. Basheleishvili
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Three Dimensional ◽  
Mixture Theory ◽  
Potential Method ◽  
Fredholm Integral Equations ◽  
Infinite Domains ◽  
Elastic Mixture ◽  
Uniqueness Of The Solution ◽  
Dimensional Boundary

Abstract The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary value problem is proved for the split equation.

An Efficient Mixed Finite Element Perfectly Matched Layer with Optimal Parameters Selection for Two-Dimensional Time Domain Soil-Structure Interaction Analysis

2021 ◽  
Author(s):  
Dong Van Nguyen ◽  
Jaemin Kim
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Soil Structure ◽  
Perfectly Matched Layer ◽  
Soil Structure Interaction ◽  
Numerical Analyses ◽  
Two Dimensional ◽  
Infinite Domains ◽  
Structure Interaction ◽  
Parameters Selection

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

Infinite Domains

1998 ◽  
pp. 193-218
Author(s):  
Alain Bossavit
Keyword(s):  
Infinite Domains
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