Mathematical Modeling and Supercomputer Technologies: 20th International Conference, MMST 2020, Nizhny Novgorod, Russia, November 23 – 27, 2020, ... in Computer and Information Science)

This book constitutes selected and revised papers from the 20th International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2020, held in Nizhny Novgorod, Russia, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 25 full papers and 8 short papers presented in the volume were thoroughly reviewed and selected from the 106 submissions. They are organized in topical secions on ​computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation. Preface Organization Contents Computational Methods for Mathematical Models Analysis Mathematical Rigor in Applied Mathematics Based on the Nonstandard Analysis 1 Introduction 2 What is the Modern Mathematical Rigor 3 Theory of Quasi-sets – A Version of NSA References Algorithms and Scenarios of Online Decision Support System for Selection of the Distribution Laws of positive Random Variables 1 Introduction 2 DSS Scenarios and Algorithms for Selecting RV Distribution Laws 3 The DSS Basic Elements 4 Conclusions References Application of the Entropic Tilt Limiter to Solve the Gas Dynamics Equations Using the Implicit Scheme of the Discontinuous Galerkin Method 1 Mathematical Model and Computational Algorithm 2 Entropic Tilt Limiter 3 Test Results 3.1 Computing Tools and Libraries Used 3.2 The Flow of an Inviscid Compressible Gas in a Flat Channel with a Wedge 3.3 Prandtl-Meyer Expansion Fan 3.4 Steady-State Oblique Shock Wave 4 Conclusion References Methods for Simulation the Nonlinear Dynamics of Gyrotrons 1 Introduction 2 Stationary Model 3 Multimode Time-Depended Model 3.1 Mathematical Formulation of the Problem 3.2 Implicit Crank—Nicolson Scheme 3.3 Approximation of the Boundary Conditions 4 Examples of Mode Competition in Gyrotrons Operating in Different Frequency Ranges 5 Conclusion References Mathematical Modeling of Multidimensional Strongly Nonlinear Dynamic Systems 1 Introduction 2 Problem Setting 3 Solution Method 4 Numerical Study of the Dynamics of a Two-Piston Vibroimpact Mechanism 5 Numerical Study of the Dynamics of a Three-Piston Vibroimpact Mechanism 6 Dynamics of the Vibroimpact Mechanism Taking into Account the Influence of the Processed Medium References Hierarchy of Models of Quasi-stationary Electromagnetic Fields 1 Introduction 2 Functional Spaces 3 Problems for Maxwell's Equations in Homogeneous Media 4 Initial-Boundary Value Problems for Maxwell's Equations in Inhomogeneous Media 4.1 The Non-stationary Maxwell's Equations System 4.2 Quasi-stationary Approximation to Maxwell's Equations 4.3 Non-relativistic Magnetic Approximation 5 Comparison of Solutions to Problems 6 Discussion References Numerical Simulation of the Wind Resonance of the Bridge Based on Scale-Resolving Approaches 1 Introduction 2 Problem Statement 3 Technique of the Amplitude Estimation Based on Scale-Resolving Simulation 4 Results and Discussion 5 Conclusion References Influence of Material Damage on the Parameters of a Nonlinear Flexible Wave Which Spread in a Beam 1 Introduction 2 Mathematical Model 3 Nonlinear Stationary Waves 4 Alternative Mathematical Model 5 Conclusion References Chaotic Change of Extracellular Matrix Molecules Concentration in the Presence of Periodically Varying Neuronal Firing Rate 1 Introduction 2 Mathematical Model 3 ECM Dynamics for Various Types of Neuronal Activity 3.1 Stable ECM-modes for Constant Levels of Neuronal Firing Rate 3.2 ECM Dynamics for Periodically Varying Neuronal Firing Rate 4 Discussion 5 Conclusions References Quiescence-to-Oscillations Transition Features in Dynamics of Spontaneous Astrocytic Calcium Concentration 1 Introduction 2 Description of the Mathematical Model 3 Results 4 Conclusions References An Architecture for Real-Time Massive Data Extraction from Social Media 1 Introduction 2 Related Work 3 Requirements and Design Approach 4 Cloud-Based Architecture and Data Model Design 4.1 Cloud-Based Architecture 4.2 Data-Model Design 5 Conclusion References Node Degree Dynamics in Complex Networks Generated in Accordance with a Modification of the Triadic Closure Model 1 Introduction 2 The Modification of the Triadic Closure Model and Its Analysis 2.1 The Model Description 2.2 The Model Analysis in Case m=2 and p=1 2.3 Node Degree Dynamics (General Case) 3 Conclusion References On a General Approach for Numerical Solving Singular Integral Equations in the Scalar Problems of Diffraction by Curvilinear Smooth Screens 1 Introduction 2 Integro-Differential Equation of the Diffraction Problem 3 Basis Functions and Galerkin Method 3.1 Numerical Tests References Noise Influence on the Estimation of Characteristics of Intermittent Generalized Synchronization Using Local Lyapunov Exponents 1 Introduction 2 Determination of Intermittency Characteristics Using Local Lyapunov Exponents 3 Estimation of Statistical Characteristics of the Intermittent GS 4 Conclusion References Application of the Kovacic Algorithm to the Problem of Rolling of a Heavy Homogeneous Ball on a Surface of Revolution 1 Introduction 2 Problem Formulation. General Equations of Motion 3 Rolling of a Ball on a Paraboloid of Revolution 4 Conclusions References Computation in Optimization and Optimal Control Optimal Rotor Stabilization in an Electromagnetic Suspension System Using Takagi-Sugeno Fuzzy Models 1 Introduction 2 Fuzzy Object Model 3 Formulation of the Problems 4 The Solving Methodology 4.1 Calculation of a Stabilizing Fuzzy Controller 4.2 Calculation of a Fuzzy γ-Optimal Controller 5 Results 6 Conclusion References Analysis of Indicators of Optimal Functioning of a Network of Hospitals, Taking into Account Errors of Observation Results 1 Introduction 2 Mathematical Model 3 Optimization of Bed Allocation 4 Conclusion References Optimal Control Problem with State Constraint for Hyperbolic-Type PDE 1 Introduction 2 The Controlled Process and Supporting Statements 3 The Optimization Problem 4 Auxiliary Initial-Boundary Value Problem 5 The Expansion of the System of Cosines 6 The Infinite-Dimensional System of Differential Equations 7 The Shortened System 8 The Study of an Optimization Problem 9 The Algorithm for Finding the Optimal Value 10 Conclusion References Numerical Investigation and Optimization of Output Processes in Cyclic Control of Conflicting Flows 1 Introduction 2 Problem Statement at the Content Level 3 Numerical Study of Output Processes 4 Conclusion References Parametric Randomization for Accelerating the Nested Global Optimization 1 Introduction 2 Global Optimization and Nested Dimensionality Reduction 3 Randomized Choice of the Algorithm's Parameter 3.1 Computational Scheme of the Algorithm 3.2 Techniques of Parameter Randomizing 4 Computational Experiments 5 Conclusion References Modeling Vertical Migrations of Zooplankton Based on Maximizing Fitness 1 Introduction 2 Materials and Methods 3 Results 3.1 Fitness Identification 3.2 Optimization Problem Solution 4 Summary References Localization of Pareto-Optimal Set in Multi-objective Minimax Problems 1 Introduction 2 Two-Sided Boundaries of a Domain Containing Pareto Optimal Points 3 H Norm with Transients 4 Synthesizing Pareto Suboptimal H Controllers with Transients 5 Illustrative Example: Vibration Isolation 6 Conclusion References Estimating a Set of the States in the Case of an Error in the Measured Output for Controlled System 1 Introduction 2 Preliminary Information 3 Formulation of the Problem 4 Estimation of the Set of Admissible Initial States 5 Numerical Simulation Results 6 Conclusions References Multicriteria Problem of Wireless System Design Using Tricriteria Approach with Qualitative Information on the Decision Maker's Preference 1 Introduction 2 Model for Making a Rational Decision on the Choice of Wireless System Parameters 3 Objects and Criteria 4 Using Designer Preferences During the Development Phase 4.1 Three-Criteria Approach 4.2 Single Criteria Approach 5 Use of Intergroup Preferences During Operation 6 Conclusion References Application of Optimal Evaluation of Linear Time-Varying Systems Using Reachable Sets 1 Introduction 2 Reachable Sets 3 Finding of Reachable Sets 3.1 Unknown Initial State Problem 3.2 Parametric Uncertainty Problem 4 Reachable Sets Evaluation in the Unknown Initial State Problem 5 Conclusion References Supercomputer Simulation M2H3D Code: Moving Mesh Hydrodynamics by Means AVX-2 Technology 1 Introduction 2 Numerical Model 3 Code 3.1 Data Structures 3.2 Grid Format 3.3 Geometry Subroutine 3.4 Physical Variables Reconstruction 3.5 Hydrodynamic Equations Solver 3.6 Poisson Solver 3.7 Vectorization 4 Numerical Example 4.1 Sedov Blast Wave 4.2 Evrard Collapse 5 Conclusions References Comparison of AMD Zen 2 and Intel Cascade Lake on the Task of Modeling the Mammalian Cell Division 1 Introduction 2 Computer Systems 2.1 Technical Specifications 2.2 Comparison of Zen 2 with Cascade Lake 2.3 Related Works 3 The Simulated Biological Process 4 Numerical Algorithm 5 Testing Methodology 6 Results and Discussion 6.1 Support for a Large Number of Cores Is Required Not Only from Applications, But Also from Operating Systems and Compilers 6.2 For Intensive Computations on a Small Number of Cores, Cascade Lake and Zen 2 Demonstrate Similar Performance 6.3 On Active Memory Operations, Cascade Lake Is Slightly Ahead of Zen 2 6.4 When the Second Socket Cores Are Used, Cascade Lake Sometimes Loses to Zen 2 7 Conclusion References Computing the Sparse Matrix-Vector Product in High-Precision Arithmetic for GPU Architectures 1 Introduction 2 Compressed Sparse Row 3 High-Precision Data Types of MPRES-BLAS 4 High-Precision SpMV for GPU 4.1 Scalar Kernel 4.2 Two-Step Implementation 5 Performance Evaluation 6 Conclusions References Performance Analysis of Deep Learning Inference in Convolutional Neural Networks on Intel Cascade Lake CPUs 1 Introduction 2 Related Work 3 Deep Learning Frameworks 4 Experimental Settings 4.1 Computational Infrastructure 4.2 Models and Data 4.3 Performance Metrics 5 Results and Discussion 5.1 Performance and Scalability Analysis of DL Inference 5.2 Performance and Accuracy of Quantized Models in OpenVINO 5.3 Performance Analysis of the Throughput Mode in OpenVINO 5.4 Final Comparison 6 Conclusions References On the Problem of Choosing the Optimal Parameters for the Wind Farm in the Arctic Town of Tiksi 1 Introduction 2 Wind Farm in the Town Tiksi 2.1 Mathematical Model in WRF-ARW Code 2.2 Numerical Domain, Grid, and Results of Calculation 2.3 Setting Task of Optimizing the Generated Capacity of the Wind Farm 3 Analytical Models for Calculation of Wake Parameters 4 Conclusion References Multidimensional Interpolation Methods in Simulation Planning for Modeling 1 Introduction 2 Problem Statement 3 Multidimensional Interpolation Method Selection 4 Pre-sampling Based on Voronoi Diagram Borders Points Estimation 5 Pre-sampling Based on Points Estimation Lying on Intersection of Voronoi Diagram Borders and Base Vectors 6 Obtaining the Next Iteration Batch's Points 6.1 Batch Points Sampling 6.2 Sampling Based on Dichotomy Method 6.3 Iterative Sampling Method 7 Algorithms Complexity 7.1 Shepard's Method Complexity 7.2 Construction of Approximated Voronoi Diagram Complexity 7.3 Obtaining Points Lying on Intersection of Voronoi Diagram Borders and Base Vectors Complexity 7.4 Sampling Based on Dichotomy Method Complexity 7.5 Iterative Sampling Method Complexity 8 Experiments 8.1 Model Experiments 8.2 Application of Algorithms for the Practical Problem of the Body Motion in a Liquid References The Optimized Finite Element Dynamical Core of the Arctic Ocean Sea Ice Model 1 Introduction 2 Building a Model Grid 3 Features of the INMOST Package 4 Optimized Method for Numerical Integration of the Sea Ice Momentum Balance with Viscous-Plastic Rheology 4.1 Governing Equations 4.2 mEVP Method 4.3 VP-Picard Method 4.4 mEVP-opt Method 4.5 Numerical Experiments 5 Conclusion References Performance of Supercomputers Based on Angara Interconnect and Novel AMD CPUs/GPUs 1 Introduction 2 Related Work 3 Hardware 4 Comparison of Angara and Infiniband FDR 5 High-Performance Linpack Benchmarks on Fisher 5.1 Comparison of Performance on Fisher's Air Segment and Fisher's Immersion Segment 5.2 Fisher Immersion Segment's Results with Epyc 7662 6 High-Performance Linpack Benchmarks on Desmos 7 Conclusion References Author Index