Parallel Scientific Computing and Optimization
Advances and Applications
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Article
On Construction and Properties of Compact 4th Order Finite-Difference Schemes for the Variable Coefficient Wave Equation
We consider an initial-boundary value problem for the n-dimensional wave equation with the variable sound speed, \(n\ge 1\) ...
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Article
Finite volume ADI scheme for hybrid dimension heat conduction problems set in a cross-shaped domain
In this paper, we construct an alternating direction implicit (ADI) type finite volume numerical scheme to solve a nonclassical nonstationary heat conduction problem set in a 2D cross-shaped domain. We reduce ...
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Chapter and Conference Paper
High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators
In this paper we develop and investigate numerical algorithms for solving the fractional powers of discrete elliptic operators ...
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Article
Modelling competition of the enzyme-catalysed glucose oxidation and redox reactions in scanning electrochemical microscopy
Kinetics of the glucose oxidation catalysed with immobilized enzyme (glucose oxidase) and redox reactions that compete for dissolved oxygen in an electrochemical cell is studied numerically by employing a mean...
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Chapter and Conference Paper
A Comparison of Accuracy and Efficiency of Parallel Solvers for Fractional Power Diffusion Problems
In this paper, we construct and investigate parallel solvers for three dimensional problems described by fractional powers of elliptic operators. The main aim is to make a scalability analysis of parallel vers...
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Article
Application of distributed parallel computing for dynamic visual cryptography
We consider one applied global optimization problem where a set of feasible solutions is discrete and very large. The goal is to find optimal perfect gratings, which can guarantee high quality and security of ...
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Chapter and Conference Paper
Modeling and Simulations of Beam Stabilization in Edge-Emitting Broad Area Semiconductor Devices
A 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presen...
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Chapter and Conference Paper
On Parallelization of the OpenFOAM-Based Solver for the Heat Transfer in Electrical Power Cables
In this work, we study the parallel performance of OpenFOAM-based solver for heat conduction in electrical power cables. The 2D benchmark problem is used for our tests. The parallelization approach used in Ope...
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Chapter and Conference Paper
Parallel Numerical Algorithms for Simulation of Rectangular Waveguides by Using GPU
In this article we consider parallel numerical algorithms to solve the 3D mathematical model, that describes a wave propagation in rectangular waveguide. The main goal is to formulate and analyze a minimal alg...
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Article
Numerical analysis of nonlinear model of excited carrier decay
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trap** states and recombination centers in the bandgap, the carrier decay process is defined by...
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Chapter and Conference Paper
Parallel Numerical Algorithms for Simulation of Multidimensional Ill-Posed Nonlinear Diffusion-Advection-Reaction Models
This paper presents finite difference approximations of two dimensional in space mathematical model of a bacterial self-organization. Due to the chemotaxis process some instability of the solution can be devel...
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Chapter and Conference Paper
Parallel Algorithms for Parabolic Problems on Graphs
In this paper two parallel numerical algorithms for solution of parabolic problems on graphs are investigated. The fully implicit and predictor-corrector finite difference schemes are proposed to approximate t...
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Article
On some finite difference schemes for solution of hyperbolic heat conduction problems
We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple sc...
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Chapter and Conference Paper
Parallel Numerical Solver for Modelling of Electromagnetic Properties of Thin Conductive Layers
In this paper we develop the parallel numerical algorithm for modelling of electromagnetic properties of thin conductive layers. The explicit finite difference scheme is obtained after approximation of the sys...
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Book
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Chapter
Parallelization of Linear Algebra Algorithms Using ParSol Library of Mathematical Objects
The linear algebra problems are an important part of many algorithms, such as numerical solution of PDE systems. In fact, up to 80% or even more of computing time in this kind of algorithms is spent for linear...
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Chapter
Parallel Multiblock Multigrid Algorithms for Poroelastic Models
The application of parallel multigrid for two-dimensional poroelastic model is investigated. First, a special stabilized finite difference scheme is proposed, which allows one to get a monotone approximation o...
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Chapter
A Parallel Solver for the 3D Simulation of Flows Through Oil Filters
The performance of oil filters used in automotive engines and other areas can be significantly improved using computer simulation as an essential component of the design process. In this chapter, a parallel so...
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Chapter
Parallel Numerical Solver for the Simulation of the Heat Conduction in Electrical Cables
The modeling of the heat conduction in electrical cables is a complex mathematical problem. To get a quantitative description of the thermo-electrical characteristics in the electrical cables, one requires a m...
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Chapter
Parallel Numerical Algorithm for the Traveling Wave Model
A parallel algorithm for the simulation of the dynamics of high-power semiconductor lasers is presented. The model equations describing the multisection broad-area semiconductors lasers are solved by the finit...
