Numerical Methods and Applications: 10th International Conference, NMA 2022, Borovets, Bulgaria, August 22–26, 2022, Proceedings

Description

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods. Preface Organization Contents SUSHI for a Bingham Flow Type Problem 1 Problem to Be Solved and the Aim of This Note 2 Space and Time Discretizations and Some Preliminaries 3 Formulation of a Finite Volume Scheme for the Problem (9)–(11) 4 Convergence Analysis of Scheme (17)–(18) 5 Conclusion and Perspectives References Two-Phase Algorithm for Solving Vehicle Routing Problem with Time Windows 1 Introduction 2 Mathematical Problem Formulation for the VRPTW 3 Our Proposed Approach for Solving the VRPTW 3.1 Utilizing the K-Means Algorithm for Customer Clustering 3.2 Seeking Exact Feasible Solutions by the CPLEX Solver 4 Experimental Analysis 5 Conclusion References Topological Dynamic Consistency of Numerical Methods for Dynamical Models in Biosciences 1 Introduction 2 Defining Topological Dynamic Consistency 3 Structural Stability and Topological Dynamic Consistency 4 Some Applications of Theorem 2 4.1 Gradient Flows 4.2 Flows with a Lyapunov Function 5 Conclusion References Parameter Estimation Inspired by Temperature Measurements for a Chemotactic Model of Honeybee Thermoregulation 1 Introduction and Model Problem 2 Inverse Problems 2.1 The IP1 2.2 The IP2 3 Numerical Method 4 Numerical Simulations References On the Consistency and Convergence of Repeated Richardson Extrapolation 1 Introduction 2 The Method of Classical and Repeated Richardson Extrapolation 3 Runge–Kutta Methods and Their Order Conditions 4 Increasing the Order by RRE 4.1 Order Increase from 1 to 3 5 Convergence Analysis for RRE 6 Conclusion References Convergence Analysis of a Finite Volume Scheme for a Distributed Order Diffusion Equation 1 Introduction 2 Space Discretization 3 Approximation of the Distributed Order Operator and Some Preliminaries 4 Statement of the Main Results of This Work 4.1 Formulation of a New Finite Volume Scheme for the Problem (1)–(4) 4.2 Unique Solvability, Stability, and Convergence Rate for Scheme (22)–(23) 5 Conclusion and Perspectives References SUSHI for a Non-linear Time Fractional Diffusion Equation with a Time Independent Delay 1 Introduction to the Problem to be Solved and Aim of This Note 2 Space and Time Discretizations and Some Preliminaries 3 Main Results of the Paper 3.1 Formulation of a Finite Volume Scheme for (1)–(4) 3.2 Convergence Order of Scheme (12)–(13) 4 Conclusion and Perspectives References On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving Uncertainties 1 Introduction: The Exponential Decay Chain 2 The Two-Step Exponential Decay-Outbreak Model: Properties 2.1 A Basic Wave-Like Function 2.2 The Basic Outbreak Function: Maximum Value and Inflection Point 3 Least-Square Approximations: Fitting the Exponential Decay Function 3.1 Fitting the Exponential Decay Function to a Numeric Data Set 3.2 Fitting the Exponential Decay Function to an Interval-Valued Data Set 4 Numerical Simulations Involving the Basic Exponential Decay-Outbreak Model 5 Concluding Remarks References Rational Approximation Preconditioners for Multiphysics Problems 1 Introduction 2 Darcy–Stokes Model 3 Mixed Finite Element Discretization 4 Rational Approximation for the General Problems of Sums of Fractional Operators 4.1 Preconditioning 5 Numerical Results 5.1 Approximating the Sum of Two Fractional Exponents 5.2 The Darcy–Stokes Problem 6 Conclusions References Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems 1 Introduction 2 Determination of Effective Moduli of Poroelastic Nanocomposites Using Homogenization Approach and Finite Element Method 3 RVE Finite Element Model 4 Numerical Results 5 Conclusion References Ant Algorithm for GPS Surveying Problem with Fuzzy Pheromone Updating 1 Introduction 2 Short Remark on Intuitionistic Fuzzy Logic 3 GPS Surveying Problem Formulation 4 ACO Algorithm with Intuitionistic Fuzzy Pheromone 5 Numerical Experiments and Discussion 6 Conclusions References Covering a Set of Points with a Minimum Number of Equal Disks via Simulated Annealing 1 Introduction 2 Converting the Problem into Unconstrained Optimization 3 Simulated Annealing Algorithm 4 Computer Experiments 5 Conclusion References Mathematical Modelling of Nonlinear Heat Conduction with Relaxing Boundary Conditions 1 Introduction 2 Physical System and Mathematical Model 3 Relaxing Boundary Condition 4 Numerical Method 5 Computer Experiments 6 Conclusion References Random Sequences in Vehicle Routing Problem 1 Introduction 2 Methodology 2.1 Monte-Carlo Method 2.2 Monte-Carlo Simulation Applied on CWS 2.3 Random Number Generators 3 Results and Experiments 4 Conclusion References A Database of High Precision Trivial Choreographies for the Planar Three-Body Problem 1 Introduction 2 Differential Equations Describing the Bodies Motion 3 Numerical Searching Procedure 4 Linear Stability Investigation 5 Numerical Results 6 Conclusions References Evaluation of the Effective Material Properties of Media with Voids Based on Numerical Homogenization and Microstructure Data 1 Introduction and Motivation 2 Methodology 2.1 Microstructure Diagnostic: Micro–CT Testing 2.2 Instrumented Indentation Testing 3 Numerical Homogenization Technique 3.1 Effective Elastic Material Properties 4 Conclusions References Variable Neighborhood Search Approach to Community Detection Problem 1 Introduction 2 Problem Formulation 3 Related Work 4 VNS Implementation 4.1 Brief Description of VNS 4.2 Implementation Details 4.3 Parameter Tuning 5 Experimental Evaluation 5.1 Experimental Setup 5.2 Parameter Settings 5.3 Comparison Results 6 Conclusion References Simulation Investigations of Pyramidal Cells Layer Effect on Conscious Visual Perception 1 Introduction 2 Model Structure 3 Simulation Results 3.1 Connectivity from RGC to FO and HO Thalamus 3.2 Presence/Absence of the Pyramidal Cells Layer L5 4 Conclusions References On Decision Making Under Uncertainty 1 Introduction 2 Statement of the Problem and Preliminaries 3 A Necessary Optimality Condition for the Existence of a Saddle Point 4 Example References An Inequality for Polynomials on the Standard Simplex 1 Introduction and Statement of the Results 2 Proofs of Theorems 1 and 2 3 Proof of Theorem 3 4 Proofs of Theorems 4 and 5 References A Theoretical Analysis on the Bound Violation Probability in Differential Evolution Algorithm 1 Preliminaries 2 Differential Evolution 2.1 Bound Constraints Handling Methods 3 Analysis for the Exponentially Confined Strategy 3.1 Related Work 3.2 Method and Assumptions 3.3 Probability Distribution Function of the Difference Term 3.4 Probability Distribution Function of the Mutant 4 Estimation of the Bound Violation Probability 5 Conclusions References On the Extreme Zeros of Jacobi Polynomials 1 Introduction and Statement of the Results 2 The Euler–Rayleigh Method 3 Proof of the Results 3.1 Proof of Theorem 1 3.2 Proof of Theorem C 4 Remarks References Sensitivity Analysis of an Air Pollution Model with Using Innovative Monte Carlo Methods in Calculating Multidimensional Integrals 1 Introduction 2 Advanced Stochastic Algorithms 3 Short Review, Parallelization and Scalability of UNI-DEM 3.1 Parallel Implementation and Optimizations 3.2 Scalability Experiments with UNI-DEM on the Bulgarian EuroHPC Petascale Supercomputer DISCOVERER 4 Sensitivity Analysis of UNI-DEM with Respect to Emission Levels 5 Sensitivity Analysis of UNI-DEM with Respect to Chemical Reaction Rates 6 Conclusions References Demanded Scale for Modern Numerical Optimisation 1 Introduction 2 Constraints and Limitations 2.1 Time Frame Requirements 2.2 Delivery Location 2.3 Zero Carbon Emissions and Vehicle Capacity 2.4 Accidental Events and Service Failure 2.5 Packets Grouping and Packing Waste 3 Optimisation Algorithms Applied to High Scale Tasks 4 Experimental Results 5 Discussion 6 Conclusion References RMSD Calculations for Comparing Protein Three-Dimensional Structures 1 Introduction 2 Root Mean Squared Distance - RMSD 2.1 Some Useful Softwares 2.2 Kabsch Algorithm ch25Kabschsps76,ch25Kabschsps1978 2.3 Quaternion Algorithm ch25McLachlansps1972,ch25WSVsps1991: 3 Conclusion References On the Application of a Hierarchically Semi-separable Compression for Space-Fractional Parabolic Problems with Varying Time Steps 1 Introduction 2 Space-Fractional Parabolic Problem 2.1 Discretizations in Space and Time 2.2 Test Problem 3 Hierarchically Semi-separable Compression Based Solver 3.1 Hierarchically Semi-separable Compression 3.2 ULV-Like Factorization and Solution 4 Complexity of Parabolic Solvers and the Test Problem 5 Comparative Analysis of Numerical Experiments 6 Concluding Remarks References Optimized Stochastic Approaches Based on Sobol Quasirandom Sequences for Fredholm Integral Equations of the Second Kind 1 Introduction 2 Biased Stochastic Approaches 2.1 Monte Carlo Algorithms Based on Modified Sobol Sequences 2.2 Stratified Symmetrised Monte Carlo Approach 2.3 Specific Modification of the Algorithms for Solving Integral Equations 3 Unbiased Stochastic Approach 4 Numerical Results 4.1 Stochastic Approach for Multidimensional Problems 5 Conclusion References Intuitionistic Fuzzy Knapsack Problem Trough the Index Matrices Prism 1 Basic Definitions of the Concepts of Index Matrices and Intuitionist Fuzzy Logic 1.1 Short Remarks on Intuitionistic Fuzzy Pairs (IFPs) 1.2 Definition, Operations and Relations with Intuitionistic Fuzzy IMs 2 Index-Matrix Interpretation of a 0-1 Intuitionistic Fuzzy KP 2.1 Format of Calculations of Index Matrix Approach to the 0-1 KP, Based on Dynamic Programming Approach 2.2 A Software Program for Optimal IFKP 2.3 A Case Study 3 Conclusion References Numerical Solutions of the Boussinesq Equation with Nonlinear Restoring Force 1 Introduction 2 Exact Solitary Wave Solutions 3 A Conservation Law 4 Finite Difference Schemes 5 Numerical Results References Simulation of the Mechanical Wave Propagation in a Viscoelastic Media With and Without Stiff Inclusions 1 Introduction 2 Geometry 3 Mathematical Formulation of the Problem 3.1 Dynamics of the Viscoelastic Continuum 3.2 Boundary and Initial Conditions 4 Transient Analysis 5 Numerical Results 6 Conclusion References Author Index