Computational Methods and Applications for Numerical Analysis

• Other Authors: Wang, Fajie (Editor), Lin, Ji (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Research & information: general; Mathematics & science; localized meshless collocation method; virtual boundary element; fundamental solution; Laplace equations; Helmholtz equations; thermo-elastic structure; topology optimization; reliability analysis; stress constraint; radial basis function; the shape parameter; multiquadric; inverse multiquadric; Gaussian; elastic-plastic problems; incremental theory; Smoothed Finite Element Method (S-FEM); Julia language; parallel programming; nonlinear elliptic equation; doubly connected domain; inverse problems; two-parameter homogenization functions; Brazilian disc test; numerical simulation; crack evolution; failure mode; indirect tensile strength; topology optimisation; piezoelectric actuator; shell; finite element method; symmetric tridiagonal matrix; eigenvalue solver; matrix division; parallel algorithm; machine learning; extrinsic; embedding; intrinsic; surfaces; Laplace-Beltrami operator; meshfree numerical technique; free vibration; integration error; numerical integration; eigenvector solver; clustered eigenpairs; orthogonalization; general Q iteration; triangulations; shortest edge; triangle shape; high-order enrichment functions; numerical methods; numerical dispersion; transient analysis; wave propagation; Bernstein-Bézier coefficients; quasi-interpolation; type-1 triangulation; Clough-Tocher split; multi-dimensional fractional equations; multi-term fractional equations; meshless method; collocation method; analytic representation; numerical analysis; structure optimization; parametric optimization; GST; chromium; SiO2; Photovoltaic applications; co-simulation; defect analysis; error bounds; variable step-size; singular boundary method; Kansa's method; heterogeneous media; acoustic wave; soil-rock mixture; lattice Boltzmann method; size effect; permeability; global-local; non-intrusive; computational simulation; crack growth; frame elements; 3D solids; coupling
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.