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Computational Methods and Applications for Numerical Analysis

Computational Methods and Applications for Numerical Analysis

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The present reprint contains the 20 articles accepted and published in the Special Issue “Computational Methods and Applications for Numerical Analysis” of the MDPI “Mathematics” journal, which surround the theory, algorithms, programming, software, numerical simulation, and/or novel applications of computational methods to solve problems in engineering, science, and other disciplines related to computations. These topics include finite element methods, finite difference methods, meshless/meshfree methods, physics-informed neural networks, interpolation, approximation, optimization, numerical methods for ordinary/partial differential equations, etc. Their applications include crack propagation, acoustic analysis, elastodynamic analysis, free vibration analysis, structure and topology optimization, fractional equations, eigenvalue problems, inverse problems, etc. Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. It is hoped that the reprint will be interesting and useful for those working in the area of numerical analysis, as well as for those with a proper mathematical background and willing to become familiar with novel applications of computational techniques, which have rapidly developed nowadays.

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Keywords

  • 3D solids
  • acoustic wave
  • analytic representation
  • Bernstein–Bézier coefficients
  • Brazilian disc test
  • Chromium
  • Clough–Tocher split
  • clustered eigenpairs
  • co-simulation
  • collocation method
  • computational simulation
  • coupling
  • crack evolution
  • Crack growth
  • defect analysis
  • doubly connected domain
  • eigenvalue solver
  • eigenvector solver
  • elastic-plastic problems
  • embedding
  • error bounds
  • extrinsic
  • failure mode
  • Finite element method
  • frame elements
  • free vibration
  • fundamental solution
  • Gaussian
  • general Q iteration
  • global–local
  • GST
  • Helmholtz equations
  • heterogeneous media
  • high-order enrichment functions
  • incremental theory
  • indirect tensile strength
  • integration error
  • intrinsic
  • inverse multiquadric
  • inverse problems
  • Julia language
  • Kansa’s method
  • Laplace equations
  • Laplace–Beltrami operator
  • Lattice Boltzmann method
  • localized meshless collocation method
  • Machine learning
  • Mathematics & science
  • matrix division
  • meshfree numerical technique
  • meshless method
  • multi-dimensional fractional equations
  • multi-term fractional equations
  • multiquadric
  • non-intrusive
  • nonlinear elliptic equation
  • Numerical analysis
  • numerical dispersion
  • Numerical integration
  • Numerical methods
  • Numerical Simulation
  • orthogonalization
  • parallel algorithm
  • parallel programming
  • parametric optimization
  • Permeability
  • Photovoltaic applications
  • piezoelectric actuator
  • quasi-interpolation
  • radial basis function
  • Reference, information & interdisciplinary subjects
  • reliability analysis
  • Research & information: general
  • Shell
  • shortest edge
  • singular boundary method
  • SiO2
  • size effect
  • Smoothed Finite Element Method (S-FEM)
  • soil–rock mixture
  • stress constraint
  • structure optimization
  • Surfaces
  • symmetric tridiagonal matrix
  • the shape parameter
  • thermo-elastic structure
  • topology optimisation
  • topology optimization
  • transient analysis
  • triangle shape
  • triangulations
  • two-parameter homogenization functions
  • type-1 triangulation
  • variable step-size
  • virtual boundary element
  • wave propagation

Links

DOI: 10.3390/books978-3-0365-8285-6

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