Mathematical Modeling and Supercomputer Technologies : 22nd International Conference, MMST 2022, Nizhny Novgorod, Russia, November 14–17, 2022, Revised Selected Papers

This book constitutes selected and revised papers from the 22nd International Conference on Mathematical Modeling and Supercomputer Technologies, MMST 2022, held in Nizhny Novgorod, Russia, in November 2022. The 20 full papers and 5 short papers presented in the volume were thoroughly reviewed and selected from the 48 submissions. They are organized in topical secions on ​computational methods for mathematical models analysis; computation in optimization and optimal control; supercomputer simulation. Preface 6 Organization 8 Contents 10 Computational Methods for Mathematical Models Analysis 13 Diffusion in the Phase Space of the Autooscillatory System, Demonstrating the Stochastic Web in the Conservative Limit: Numerical Investigation 14 1 Introduction 14 2 Methods of the Investigation 15 3 Dependence of Average Ensemble Energy on Time 20 4 Conclusion 24 References 25 Aberrator Shape Identification from 3D Ultrasound Data Using Convolutional Neural Networks and Direct Numerical Modeling 26 1 Introduction 26 2 Direct Problem 28 2.1 Problem Statement 28 2.2 Mathematical Model and Numerical Method 28 2.3 Numerical Results for the Direct Problem 29 3 Inverse Problem 32 3.1 Problem Statement 32 3.2 Neural Network Architecture 32 3.3 Dataset and Training 33 4 Numerical Experiments and Discussion 34 5 Conclusions and Future Work 38 References 38 Complex Dynamics of the Implicit Maps Derived from Iteration of Newton and Euler Methods 40 1 Introduction 40 2 Basic Model 42 3 Numerical Simulation 43 3.1 Repellers 43 3.2 Attractors 45 4 Conclusion 50 References 50 Recognition of Vertical Migrations for Two Age Groups of Zooplankton 52 1 Introduction 52 2 Materials and Methods 54 3 Results 56 3.1 Fitness Identification 56 3.2 Neural Network 58 3.3 Construction of the Training Sample 58 4 Summary 61 References 62 Nonintegrability of the Problem of Motion of an Ellipsoidal Body with a Fixed Point in a Flow of Particles 66 1 Introduction. V.V. Kozlov's Theorem on the Nonexistence of Analytic First Integral Near the Equilibrium Position of Hamiltonian System 66 2 Formulation of the Problem. Hamilton Function of the Problem 68 3 Application of V.V. Kozlov's Theorem 1 70 4 Conclusions 76 References 77 Numerical and Analytical Investigation of the Dynamics of a Body Under the Action of a Periodic Piecewise Constant External Force 78 1 Introduction 78 2 Problem Setting 80 3 Solution Method 80 4 Numerical Study of the Dynamics of a Body 87 5 Conclusion 90 References 91 Motif of Two Coupled Phase Equations with Inhibitory Couplings as a Simple Model of the Half-Center Oscillator 93 1 Introduction 93 2 The Model 94 3 The Results 96 3.1 Maps of Temporal Patterns 96 3.2 Analytical Study of Bifurcation Transitions 99 4 Conclusion 104 References 104 Solutions of Multidimensional Hydrodynamic Evolution Equations Using the Fast Legendre Transformation 106 1 Introduction 106 2 Evolution Equations of Multidimensional Flows and Growth of Surfaces 107 3 Results of Numerical Simulation of Surface Growth and Multidimensional Velocity Field Using the Two-Dimensional Fast Legendre Transform Algorithm 109 3.1 Using the Fast Legendre Transform for the Numerical Calculation of Evolutionary Nonlinear Equations 109 3.2 Results of Numerical Simulation 111 References 116 An Iterative Method for Solving a Nonlinear System of the Theory of Radiation Transfer and Statistical Equilibrium in a Plane-Parallel Layer 117 1 Introduction 117 2 Problem Statement and Main Results 118 3 Proofs of Theorems 121 3.1 Preliminary Statements 121 3.2 Proof of Theorem 3 123 3.3 Proof of Theorems 1, 2 124 4 Numerical Solution of the Transfer Equation 125 4.1 Difference Approximation of the Kinetic Equation 125 4.2 Properties of the Difference Dcheme 127 5 Computational Results 128 References 130 Role of Abnormal Calcium Signaling and Liver Tissue Structure in Glucose and Lipid Metabolism: Mathematical Modeling 132 1 Introduction 132 1.1 Main Processes 132 1.2 Hormonal Regulation 133 1.3 Calcium Regulation 135 1.4 Mathematical Models 136 2 Model Description 137 3 Results 139 4 Discussion 142 References 143 On the Period Length Modulo p of the Numerators of Convergents for the Square Root of a Prime Number p 147 1 Introduction 147 2 Preliminaries 147 3 The Main Result 150 4 Related Works 157 5 Conclusion 157 References 158 Investigation of a Queueing System with Two Classes of Jobs, Bernoulli Feedback, and a Threshold Switching Algorithm 159 1 Introduction 159 2 The Problem Statement 160 3 Essays on Solving the Stationary Equations 161 3.1 Priority Algorithm (Case L=0) 166 3.2 Case L =1 167 3.3 Some Observations Concerning the Case L=2 168 3.4 Numerical Example 169 References 170 Coexistence of Dissipative and Conservative Regimes in Unidirectionally Coupled Maps 171 1 Introduction 171 2 Model Description 172 3 Jacobian of System 174 4 Conclusion 176 References 177 Regulation of Neural Network Activity by Extracellular Matrix Molecules 178 1 Introduction 178 2 Materials 179 2.1 Mathematical Model of Single Neuron 179 2.2 Mathematical Model of ECM 180 3 Results 181 3.1 Neural Network 181 3.2 Quasi-synchronous Neural Network Activity 181 4 Conclusion 184 References 184 Investigation of Ice Rheology Based on Computer Simulation of Low-Speed Impact 187 1 Introduction 187 2 Problem Formulation 188 3 Simulation Results 190 4 Conclusion 194 References 195 Computation in Optimization and Optimal Control 196 Global Optimization Method Based on the Survival of the Fittest Algorithm 197 1 Introduction 197 2 Materials and Methods 198 2.1 Differential Evolution 198 2.2 The New Algorithm SoFDE 200 3 Results 202 3.1 Convergence Proof for SoFDE 202 3.2 Comparison of Evolutionary Algorithms 206 4 Summary 209 References 209 Solving of the Static Output Feedback Synthesis Problem in a Class of Block-Homogeneous Matrices of Input and Output 212 1 Introduction 212 2 Formulation of the Problem 213 3 Synthesis of Controllers in a Class of Block-Homogeneous Input and Output Matrices 214 4 Synthesis of Controllers with Arbitrary Input and Output Matrices 219 5 Conclusion 223 References 223 Weak Penalty Decomposition Algorithm for Sparse Optimization in High Dimensional Space 225 1 Introduction 225 2 Weak Penalty Decomposition Method in Hilbert Spaces 227 2.1 The Cardinality Constrained Optimization Problem 227 2.2 The Weak Penalty Decomposition Algorithm 227 2.3 Convergence Analysis 229 2.4 Empirical Results 231 3 Conclusion 233 References 234 Mathematical Modelling and Optimization of Scheduling for Processing Beet in Sugar Production 237 1 Introduction 237 2 Mathematical Model and Statement of the Problem 239 3 Optimal Scheduling 240 3.1 Does Mixing Beet Varieties Lead to Maximizing the Objective Function? 240 3.2 ``Hungarian Algorithm'' for Solving the Optimization Problem 241 3.3 Analytical Solutions 242 4 Numerical Results 243 5 Conclusion 247 References 247 Integration of Information Systems Data to Improve the Petroleum Product Blends Quality 249 1 Introduction 249 2 Experiment 251 3 Results and Discussions 253 4 Conclusion 258 References 258 Supercomputer Simulation 261 High-Performance Graph Coloring on Intel CPUs and GPUs Using SYCL and KOKKOS 262 1 Introduction 262 2 Background and Related Work 263 3 Implementation of Coloring Algorithms on OpenMP, SYCL and KOKKOS 266 3.1 Overview 266 3.2 Implementation on C++ 266 3.3 Implementation on SYCL 266 3.4 Implementation on KOKKOS 267 3.5 Optimizations 267 4 Numerical Results 270 4.1 Preliminaries 270 4.2 Experiments on CPU 270 4.3 Experiments on GPU 271 5 Conclusion 272 References 273 Automated Debugging of Fragmented Programs in LuNA System 275 1 Fragmented Programs and the LuNA System 275 2 Errors in the LuNA-Programs 277 3 Methods and Tools of Automated Debugging. The Analysis of Applicability to the LuNA 280 4 The Tool for Analysis Hangups of the LuNA-Programs 282 5 Overhead Evaluation 285 6 Conclusion and Future Work 287 References 288 Multi-GPU GEMM Algorithm Performance Analysis for Nvidia and AMD GPUs Connected by NVLink and PCIe 290 1 Introduction 290 2 Related Work 292 3 Performance Model Overview 292 4 Testing Platforms 293 5 Results 295 6 Discussion 295 7 Conclusions 300 References 300 Numerical Simulation of Quantum Dissipative Dynamics of a Superconducting Neuron 302 1 Introduction 302 2 Phisical Model 303 3 Numerical Implementation and Acceleration 305 4 Conclusion 309 References 310 Using Coarray Fortran for Design of Hydrodynamics Code on Nested Grids 311 1 Introduction 311 2 Numerical Model 312 3 Parallel Implementation 313 4 Sedov's Blast Wave Problem 316 5 Conclusions 317 References 317 Author Index 319