Impact of Scientific Computing on Science and Society

Foreword
Preface
Contents
Contributors
Mathematical and Numerical Modeling
On Extreme Computational Complexity of the Einstein Equations
	1 Historical Facts of Importance
	2 Exterior and Interior Schwarzschild Solution
	3 Einstein Equations of General Relativity
	4 Explicit Form of the First Einstein Equation
	5 Computational Complexity of the Einstein Equations
	6 Concluding Remarks
	References
Systematic Imposition of Partial Differential Equations in Boundary Value Problems
	1 Introduction
	2 Formal Sum of p-Forms
	3 Differential Operator for General Fields
		3.1 Hodge Operator and Wedge Product
		3.2 Action
		3.3 Differential Operator in Space-time
		3.4 Differential Operator in Space and Time
	4 Instantiation of Particular Models
		4.1 Electromagnetism
		4.2 Schrödinger Equation
		4.3 Elasticity
		4.4 Yang-Mills Equation
	5 Approximations in Finite Dimensional Spaces
	6 Conclusions
	References
Curiously Empty Intersection of Proof Engineering and Computational Sciences
	1 Introduction
	2 Unfit for Computational Sciences?
	3 Closer Investigation
		3.1 Architecture of Interactive Theorem Provers
		3.2 Theoretical Background
		3.3 Role of Elaboration
		3.4 Proof Engineering by Example
	4 Unexploited Opportunities?
		4.1 Reasons to Get Excited
		4.2 Reasons to Remain Skeptical
	5 Conclusions
	References
Challenges for Mantle Convection Simulations at the Exa-Scale: Numerics, Algorithmics and Software
	1 Introduction
	2 Geophysics
		2.1 Significance and Physics of Mantle Convection
		2.2 Challenges and Future Directions
	3 Mathematics
		3.1 Basic Components of Finite Element Simulations
		3.2 Two-Scale Surrogate
		3.3 All-at-Once Multigrid Method
	4 High Performance Computing
		4.1 Grand Challenge Problems
		4.2 Scalability Taken Seriously
		4.3 Asymptotically Optimal Not Necessarily Good Enough
		4.4 With Matrix-Free Multigrid Methods Towards Extreme Scale
		4.5 Quest for Textbook Efficiency
	5 Conclusions
	References
Remarks on the Radiative Transfer Equations for Climatology
	1 Introduction
	2 Radiative Transfer Equations for a Stratified Atmosphere
	3 Effect of Absorption Coefficient on Atmospheric Temperature
	4 Unaffected Sunlight?
	5 Earth Albedo
	6 General Statement About Earth Albedo
		6.1 Energy Type Estimate for the Grey Problem
		6.2 Frequency Dependent Case
	7 Calculus of Variations for the ν-dependent Case
		7.1 Support of the Conjecture
		7.2 Numerical Simulations
	References
Simulation and Its Use in Additive Manufacturing
	1 General Background
	2 Additive Manufacturing in 3D Printing
		2.1 L-PBF and DED Techniques
		2.2 DfAM
	3 Incorporation of Simulation in DfAM
		3.1 Simulation Process
		3.2 Different Simulation Approaches
	4 State-of-the-Art in AM Simulation
	5 Speculations About the Future Usability of the Simulation
	References
A Posteriori Error Estimates for Domain Decomposition Methods
	1 Introduction
	2 Fully Guaranteed a Posteriori Error Estimates
	3 Domain Decomposition Methods for the Basic Elliptic Problem
		3.1 Problem Formulation
		3.2 Schwarz Alternating Method
	4 Guaranteed Bounds of Errors
		4.1 A Posteriori Error Estimate Adapted to DDM
		4.2 Computation of Admissible Flux Fields
	5 Numerical Evidence
	References
Optimization and Control
Multi-criteria Problems and Incompleteness of Information in Structural Optimization
	1 Introduction
	2 Prototype Problem
	3 Multi-criteria Optimization of a Beam with a Crack System
	4 Optimization of Shell with Uncertainties in Damage Characteristics
	5 Conclusion
	References
Stability in Discrete Games with Perturbed Payoffs
	1 Introduction
	2 Basic Definitions and Notations
	3 Auxiliary Lemma and Statements
	4 Main Result
	5 Other Results
	6 Conclusion
	References
Optimal Control Problems in Nonsmooth Solid and Fluid Mechanics: Computational Aspects
	1 Introduction
	2 Identification of the Slip Bound in the Stokes System with Nonsmooth Slip Conditions
	3 Optimal Surface Coating Governed by the Stokes System with Threshold Slip Boundary Conditions
	4 Conclusions
	References
Optimal Control Approaches in Shape Optimization
	1 Introduction
	2 Distributed Penalization of the State System
		2.1 Dirichlet Conditions
		2.2 Neumann Conditions
	3 Hamiltonian Approach in Dimension Two
	References
Optimal Factor Taxation with Credibility
	1 Introduction
	2 Households and Public Sector
	3 Production and Investment
	4 Non-Credible Public Policy
	5 Savers
	6 Government
	7 Policy Rules
	8 Conclusions and Extensions
		8.1 Endogenous Fertility
		8.2 Endogenous Mortality
	References
Transformative Direction of R&D  into Neo Open Innovation
	1 Introduction
	2 Development of the Digital Economy
		2.1 R&D-Driven Growth
		2.2 Dilemma Between R&D Expansion and Declining Productivity
	3 Neo Open Innovation
		3.1 Self-Propagating Function
		3.2 Spinoff to Uncaptured GDP
		3.3 Soft Innovation Resources
		3.4 Concept of Neo Open Innovation
	4 Conclusion
	References
On Tetrahedral and Square Pyramidal Numbers
	1 Introduction
	2 Main Theorem
	3 Proof of the Main Theorem
		3.1 Proof with Even n
		3.2 Proof with Odd n
	4 Weird Numbers
	References
AI and Applications in Health Care
Randomized Constructive Neural Network Based on Regularized Minimum Error Entropy
	1 Introduction
	2 Incremental Extreme Learning Machine
	3 Proposed Method
		3.1 Problem Formulation
		3.2 Problem Solving
	4 Experimental Results
		4.1 Comparison of RMSE-MEE-RCNN with IELM
		4.2 Comparison of RMSE-MEE-RCNN with ELM, B-ELM And MLP-MEE
	5 Conclusion
	References
On the Role of Taylor\'s Formula in Machine Learning
	1 Introduction
	2 Methods
		2.1 Basic Formulations
		2.2 Taylor\'s Formula
		2.3 Autoencoder Inspired by Taylor\'s Formula
		2.4 Feature Selection Method Based on Taylor\'s Formula
	3 Computational Experiments
		3.1 Experimental Setting
		3.2 Additive Autoencoder Inspired by Taylor\'s Formula
		3.3 Feature Selection for a Distance-Based Classifier
	4 Conclusions
	References
Computational Methods in Spectral Imaging
	1 Introduction
	2 Noise Reduction
	3 Model-Based Analysis
	4 Machine Learning
	5 Applications
	6 Concluding Remarks
	References
Method for Radiance Approximation  of Hyperspectral Data Using Deep Neural Network
	1 Introduction
	2 Methods
		2.1 Dataset and Network Architecture
		2.2 Training
	3 Results
	4 Discussion
		4.1 Findings
		4.2 Related Work
	5 Conclusions
	References
Directional Wavelet Packets for Image Processing
	1 Introduction
	2 Quasi-analytic Directional Wavelet Packets
		2.1 Properties of qWPs
		2.2 Implementation Scheme for 2D qWP Transforms
		2.3 Summary of 2D qWPs
	3 Numerical Examples
		3.1 Image Denoising
		3.2 Image Inpainting
	4 Discussion
	References
Trends in Scientific Computing
Fifty Years of High-Performance Computing in Finland
	1 Introduction
	2 History
		2.1 From Centralized Systems to Computing Ecosystem
		2.2 Development of CSC
		2.3 Towards the European HPC Ecosystem
	3 Future Developments
		3.1 Prerequisites for Success
		3.2 LUMI in Kajaani
		3.3 ELIXIR and National Nodes
		3.4 LUMI\'s Eco-efficiency
	4 Conclusions
Quantum Scientific Computing
	1 Introduction
	2 Quantum Computing in a Nutshell
	3 Quantum Algorithms for Scientific Computing
		3.1 Quantum Linear Solver Algorithms
		3.2 Hybrid Quantum-Classical Algorithms
		3.3 Quantum Algorithms for Partial Differential Equations
	4 Opportunities for Scientific Quantum Computing
	References
Quantum Computing at IQM
	1 Introduction to Quantum Technology
	2 Overview of Quantum Computing
		2.1 History of Quantum Computing
		2.2 Differences Between Quantum and Classical Computing
	3 Basics of Quantum Computing Theory
		3.1 Qubit
		3.2 Quantum Information Processing
		3.3 Quantum Algorithms
	4 Quantum Computing at IQM
		4.1 IQM Technology
		4.2 Co-design Quantum Computers and Their Components
	5 Future Outlook at IQM
	References
Contribution of Scientific Computing in European Research and Innovation for Greening Aviation
	1 Introduction
	2 Technologies to Reduce Aircraft Drag
		2.1 Drag Reduction by Laminar Flow and Flow Control
		2.2 High Lift Design for Transonic Wings
		2.3 Research on Shock Wave Boundary Layer Interaction
	3 Aeroacoustic Research to Reduce Aircraft Noise
		3.1 Low-Noise Technologies for Propulsion Systems
		3.2 Airframe Noise Reduction Research
	4 Computational and Numerical Methods in Aeronautics
		4.1 Development of Reynolds Averaged Navier-Stokes (RANS) Flow Solvers
		4.2 Numerical Methods for Industrial Needs
	5 European Scientific Networks in Flow Physics and Design Methods
	6 Conclusions
	References
Thirty Years of Progress in Single/Multi-disciplinary Design Optimization with Evolutionary Algorithms and Game Strategies in Aeronautics and Civil Engineering
	1 Introduction and Motivation
	2 Methods of Design Optimization
		2.1 Evolutionary Methods Genetic Algorithms and Evolutionary Algorithms
		2.2 Multi-objective Optimization and Game Theory
		2.3 Advanced Methods and Tools for EAs
	3 Progress of the Use of Optimization Methods in Aeronautical Engineering Design
		3.1 Period 1994–2004
		3.2 Period 2004–2014
		3.3 Period 2014–2022
	4 Applications to Civil Engineering Design
	5 Conclusions and Perspectives
	References