Mesh Methods for Boundary-Value Problems and Applications: 13th International Conference, Kazan, Russia, October 20-25, 2020

Preface
Contents
Quantum Algorithms for String Processing
1 Introduction
2 Preliminaries
2.1 Rolling Hash for Strings Comparing
2.1.1 Rolling Hash
2.1.2 Fingerprinting Technique for Comparing Strings
2.1.3 Comparing Strings Using a Rolling Hash
2.2 Problems
2.3 Basics of Quantum Computation and Computational Model
3 Quantum Algorithm for String Matching Problem
3.1 Grover's Search Algorithm
3.2 Our Algorithm
3.2.1 Unique Target Case
3.2.2 Multi-Target Case
4 Quantum Algorithm for String Comparing Problem
4.1 The Algorithm Based on Grover's Search Algorithm
4.1.1 Dürr-Høyer Minimum Search Algorithm
4.1.2 The Main Part of the Algorithm
4.2 The Algorithm Based on Binary Search
5 Conclusion
References
Multicriteria Optimization Techniques in SVM Method for the Classification Problem
1 Introduction
2 Optimization Problem of SVM in a Multicriteria Formulation
3 Application of the SVM Method for Multiclass Classification Problem
4 Dataset UNSW-NB15
5 Multiclass Classification Experiments
6 Conclusion
References
Developing Experimental–Numerical Methods for Constructing True Deformation Diagrams of Elastoplastic Materials
1 Introduction
2 The Experimental–Numerical Approach
3 Constructing Deformation Diagrams of Elastoplastic Rods Loaded in Tension
4 Modification of the Algorithm of Constructing Deformation Diagrams
References
Cubic Spline on a Bakhvalov Mesh in the Presence of a BoundaryLayer
1 Introduction
2 Formulation of the Problem and Main Results
3 Auxiliary Results
4 Proof of Theorems
5 Results of Numerical Experiments
6 Conclusion
References
On Exact Penalty Operators and Penalization Methods for Elliptic Unilateral Problems with Piecewise Smooth Obstacles
1 Introduction
2 Formulation of the Problem
2.1 Functional Spaces
2.2 Original Obstacle Problem
2.3 Restrictions on the Operator A
2.4 Restrictions on the Obstacle
3 Equivalent Inequality Without Constraints
3.1 Exact Penalty Operators
4 The Penalty Problem
4.1 Examples of Penalty Functions
References
Accurate Simulation of Guided Waves in Optical Fibers Using Finite Element Method Combined with Exact Non-reflecting Boundary Condition
1 Introduction
2 Theoretical Background
3 Numerical Results
3.1 Circular Waveguide
3.2 Square Waveguide
3.3 Rectangular Waveguide
3.4 Three Circle Shaped Waveguide
References
Simulation of Dynamic Response at Resonant Vibrations of a Plate with a Viscoelastic Damping Coating
1 Introduction
2 Rectangular Finite Element with Viscoelastic Damping Coating
3 Formation of Solving Equations System
4 Determination of Stress Amplitudes in Finite Elements Under Resonant Vibrations of a Plate
5 Numerical Experiments
References
The Limit Theorem on the Trajectories Distribution
1 Introduction
2 Statement and Proof of Results
3 Conclusion
References
Design of the Best Linear Classifier for Box-Constrained Data Sets
1 Introduction
2 The Minkowski Difference of Two Sets with Box-Constrained Structure
3 Calculation of Normal Vectors for a Binary Linear Classifier
4 A Linear Classification Model
5 Conclusions
References
Patient-Specific Bone Organ Modeling Using CT Based FEM
1 Introduction
2 Materials and Methods
2.1 The Main Relations of the Finite Element Method
2.2 Digital Prototype
2.3 Integration Based on Computed Tomography Data
2.4 Stress-Strain State
2.5 Error Estimation
3 Results and Discussion
3.1 Meshing
3.2 Scanning
3.3 Modeling
3.4 Solution
3.5 Error Estimation
4 Conclusion
References
Parallel Algorithm for Solving Problem of Electromagnetic Wave Diffraction by a Tooth-Shaped Plate
1 Introduction
2 Diffraction Problem Statement
3 The Method of Moments
3.1 Basis and Testing Functions
3.2 Obtaining the System of Linear Algebraic Equations
4 Algorithm for Solving the Problem
5 Numerical Results
6 Conclusions
References
On Convergence of Explicit Differential Scheme for Solving One Parabolic Equation with Double Degeneration and Nonlocal Space Operator
1 Statement of the Problem
2 Auxiliary Results and Notation
3 Construction and Investigation of an Explicit Difference Scheme
References
The Program System for Design Optimization of Data Transmission Networks
1 Introduction
2 The Process of Data Transmission Networks Optimization
3 The Data Transmission Networks Design Optimization System
4 The Estimating Quality and Efficiency of the Data Transmission Networks
5 Mathematical Models and Methods for Data Transmission Networks Design Optimization
6 An Example of Integrated DTN Modeling
7 The DTN DOS as Basis of Electronic Scientific and Educational Complex (ESEC)
8 Conclusion
References
Mathematical Modeling of Transient Processes in Circular Channel with the Boiling of Refrigerant-113
1 Introduction
2 Mathematical Two-Fluid Model for Subcooled Boiling
3 Numerical Results
4 Conclusion
References
Hybrid Methods for Network Equilibrium Problems
1 Introduction
2 Preliminaries
3 Network Equilibrium Problems
4 Hybrid Methods for Network Equilibrium Problems
4.1 A Hybrid Methods with Inexact Direction Finding
4.2 A Hybrid Method with Adaptive Step-Size
5 Numerical Tests
6 Conclusion
References
Numerical Simulation of Water-Oil Inflow into the Producing Well from Non-uniform Oil Reservoir
1 Introduction
2 Mathematical Model
3 Numerical Model and Algorithm
4 Results
5 Conclusions
References
On Error Control at Numerical Solution of Forth Order Elliptic Equations with Strongly Discontinuous Reaction Coefficient
1 Introduction
2 C1-Conform Finite Element Method for Primal Problem
3 Ciarlet-Raviart Mixed Metod
References
On the Solvability of a One-Dimensional Problem of Filtration Consolidation with a Limiting Gradient
1 Introduction
2 Problem Statement
3 Defining a Generalized Solution
4 Existence Theorem
References
Mathematical Modeling (Faedo–Galerkin Method, Solution Existence Theorem) of Nonlinear Dynamics for MEMS/NEMS Devices Elements (Micropolar Theory) in the Rectangular Shells form in Plane, Taking into Account the Temperature and Deformation Fields Connection
1 Introduction
2 Formulation of the Problem
3 The Main Stages of the Theorem Proof
3.1 Construction of an Approximate Solution
3.2 The Priori Estimates
3.3 Transition to Limit
References
Component-Based Software Model for Numerical Simulation of Constrained Oscillations of Liquid Drops and Layers
1 Introduction
2 Mathematical Model and Numerical Method
2.1 Liquid Dynamic Equations
2.2 Advection of Indicator Function
2.3 Calculation of Interface Curvature and Normal Vector
2.4 Equation of Motion for Elastodynamics of the Plate
3 Programming Model
4 Results and Discussion
References
Modeling of Long-Term Strength of a Rod Under Creep Conditions and Finite Deformations
1 General Model
2 Tension of the Circular Cross-Section Rod
2.1 Analitical Solution of the Problem (7)–(8)
3 Conclusion
References
Locally One-Dimensional Schemes for Quasilinear Parabolic Equations with Time Fractional Derivative
1 Introduction
2 Differential Problem
3 Approximation
4 Stability and Accuracy Estimates
5 Numerical Results
6 Conclusions
References
Enhanced Step-Wise Approximation to Speech File in a Noisy Environment
1 Introduction
2 Optimal Thresholds
3 Practical Evaluation of Optimal Thresholds for Speech Files Fragments
3.1 Reduction to the Case of a Single Threshold
3.2 Evaluation of Suboptimal Thresholds Employing Linear Regression
4 Linear Regression to Enhance the Perception of the Step-Wise Signal
4.1 Distribution of Input Signals for Regression
4.2 Linear Regression and Training Procedure
5 Speech Transfer in a Noisy Environment
5.1 Preparation of Step-Wise File for Transmitting
5.2 Transmission and Restoration
References
Simulation of Two-Phase Flow Toward a Horizontal Multistage Hydraulically Fractured Well Using Accelerated Explicit-Implicit Algorithms
1 Introduction
2 Problem Statement
3 Explicit and Implicit Finite Volume Schemes
4 Numerical Solution Algorithms
5 Model Problem
6 Computational Efficiency of an Explicit-Implicit Scheme
7 Conclusion
References
Dynamical Processes in the Space of φ-Distributions
1 Introduction
2 Mathematical Model of the Problem
3 Fourier Series Expansion of the Problem's Solution
References
An Approach to Synthesis of the Neuromorphic Functional Models for Analog Components and Blocks
1 Introduction
2 Functional Models of Analog Components and Analog Circuits
3 The Design Flow of Automated Synthesis of the Neuromorphic Functional Model for Analog Active Components
4 Experimental Results
5 Conclusion
References
Scalability Pipelined Algorithm of the Conjugate Gradient Method on Heterogeneous Platforms
1 Introduction
2 Pipelined Algorithm of the Conjugate Gradient Method
3 CG with the Combined Use of CPU and GPU
3.1 Matrix Partitioning
3.2 Block Pipelined Algorithm
3.3 MPI+OpenMP+CUDA Programming Model
4 Numerical Experiments
4.1 Benchmarking with HPCG Matrices
4.2 Benchmarking on the SuiteSparse Matrix Collection
5 Conclusion
References
Accumulation of Microdamages During Cyclic Loading of CFRP Structure Elements
1 Introduction
2 Experimental Results
3 Constitutive Relations and Identification of Their Parameters
4 Conclusion
References
Two-Dimensional Integrating Matrices for Solving Elasticity Problems in a Rectangular Domain by the Finite Sum Method
1 Introduction
2 Two-Dimensional Integrating Matrices
3 Application of Two-Dimensional Integrating Matrices for Solving a Plane Stress Problem of the Theory of Elasticity in a Rectangular Domain
4 Conclusion
References
On Resonant Effects in the Semi-Infinite Waveguides with Barriers
1 Introduction
2 Lateral Barrier in a Waveguide
3 Computing Experiments, I
4 Longitudinal Barrier in a Waveguide
5 Computing Experiments, II
6 Conclusion
References
Numerical Simulation of Composite Structures Polymerization and Determination of Residual Deformations
1 Introduction
2 Numerical Simulation
2.1 Geometry and Model Parameters of the Sample
2.2 Material Model Description
2.3 Boundary Conditions
3 Analysis of the Curing Process and Stress-Strain State
3.1 Mesh Convergence
4 Production and Geometry Control of Full-Scale Samples
4.1 Accounting for Predicted Distortion of the Sample in a Mold Geometry
5 Estimation of Simulation Time
6 Conclusion
References
Numerical Analysis of One Two-layer Completely Conservative Difference Scheme of Gas Dynamics in Eulerian Variables with Adaptive Viscosity
1 Introduction
2 Completely Conservative Differential Difference Scheme
3 Approximation and Introduction of Artificial Viscosity
4 About the Iterative CCDS Algorithm Mechanism
5 Algorithm Testing
6 Conclusion
References
Accurate Simulation of On-Threshold Modes of Microcavity Lasers with Active Regions Using Galerkin Method
1 Introduction
2 GCFEP and Turned Inside Out GCFEP
3 Eigenvalue Problem for Muller BIEs
4 Galerkin Method
5 Numerical Results
6 Conclusion
References
A Solution of Inverse Problem in the Theory of Supercritical Fluid Extraction of Oil from Ground Plant Material
1 Introduction
2 Forward Problem
2.1 Problem Formulation
2.2 Problem Solution
3 Inverse Problem
3.1 Problem Formulation: Analytical Solution for Flat Particles
3.2 Numerical Algorithm for the Case of Spherical Particles
4 Test Runs
5 Conclusions and Future Work
References
Mathematical Model of a Dynamically Loaded Thrust Bearing of a Compressor and Some Results of Its Calculation
1 Introduction
2 Formulation of the Problem: Non-stationary PTEHD Model
3 Calculation Results
4 Conclusion
References
Approximation of Positive Semidefinite Nonlinear EigenvalueProblems
1 Introduction
2 Statement of the Problem
3 Parameter Problem
4 Existence and Properties of Solutions
5 Approximation of the Problem
6 Existence of Approximate Solutions
7 Convergence Analysis
8 Error Investigation
References
Numerical Modelling of the Hydraulic Fracturing Through Microseismic Monitoring
1 Introduction
2 Numerical Method
3 The Results of the Numerical Modelling for the Hydraulic Fracturing Problem
4 Discussion
5 Conclusions
References
Modeling of Deformation of Solids with Material Damage
1 Introduction
2 Solving Algorithm
3 Numerical Examples
4 Conclusion
References
Prediction of Temperature-Dependent Processes in Multicomponent Fluid Flow Through Porous Media
1 Introduction
2 State of the Art in the Research Field
3 Background of the Research
4 Governing Model
5 Computational Algorithm
6 Test Predictions
6.1 Heat Pipe Effect Simulation
6.2 Filtration of Three-Phase Fluid in a Differentially Heated Cavity
7 Conclusion
References
A Difference Scheme Based on the Schwarz Method for a Time-Dependent Singular Perturbation Problem in a Doubly Connected Domain
1 Introduction
2 Problem Formulation
3 A Priori Estimates for the Solution and Derivatives
4 Difference Schemes
4.1 Simply Connected Case
4.2 Doubly Connected Case
5 Domain Decomposition Schemes
5.1 Continual Domain Decomposition Scheme
5.2 Difference Domain Decomposition Scheme
6 Conclusion
References
Two Finite Volume Schemes for Advection Equation
1 Introduction
2 The Differential Problem
3 The Local Conservation Law
4 The First Scheme: Approximation of the Curvilinear Domain
5 The Second Scheme: Decomposition of Operator
6 Conclusion
References
Mathematical Modeling and Diagnostics Using Neural Networks and a Genetic Algorithm for Epilepsy Patients
1 Introduction
2 Neural Network
3 Genetic Algorithm
4 Approach Implementation
4.1 Object of Study
4.2 Crossbreeding and Mutations
4.3 Neural Network Configuration
5 Results and Conclusions
References
A Two-Stage Cutting-Plane Method for Conditional Minimizing Function
1 Introduction
2 Problem Settings
3 Minimization Method
References
Self-Consistent Model of Low Pressure Inductively Coupled RF Discharge
1 Introduction
2 Formulation of the Problem
3 System of Equations as a Self-Consistent Eigenvalue Problem
4 Results of Calculation
5 Conclusions
References
Robust One/Two-Grid Solver for Black-Box Software in the Computational Continuum Mechanics
1 Introduction
2 Computational Grids and Basic One-Grid Algorithm
3 Linear One/Two-Grid Solver
3.1 Globally Structured Grids
3.2 Locally Structured Grids
4 Conclusion
References
Large Deformations of Biaxial Tension-Compression of the Plate, Consisting Two Pre-deformed Layers Made of Incompressible Treloar Material
1 Introduction
2 The Generalized Statement of Problem
3 The Initial Deformation of Panels
4 The Additional Deformation of the Composite Plate
5 Numerical Results
6 Conclusion
References
Index