A wavelet Galerkin method employing B-spline bases for solid mechanics problems without the use of a fictitious domain

DOI10.1007/s00466-011-0671-9zbMath1312.74060OpenAlexW1983028405MaRDI QIDQ1937038

Satoyuki Tanaka, Shigenobu Okazawa, Hiroshi Okada

Publication date: 11 February 2013

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-011-0671-9

zbMATH Keywords

finite element methodwavelet Galerkin methodadaptive analysisstress concentration problemB-spline scaling/wavelet functions

Mathematics Subject Classification ID

Stress concentrations, singularities in solid mechanics (74G70) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Spectral and related methods applied to problems in solid mechanics (74S25)

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Cites Work

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• Synchronized reproducing kernel interpolant via multiple wavelet expansion
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Applications of wavelet Galerkin FEM to bending of beam and plate structures
• Moving least-square reproducing kernel method. II: Fourier analysis
• The partition of unity finite element method: basic theory and applications
• Adaptive multiscale wavelet-Galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization.
• Solving three-dimensional layout optimization problems using fixed scale wavelets
• Meshfree Particle Methods
• A spline wavelet finite-element method in structural mechanics
• A Cardinal Spline Approach to Wavelets
• Ten Lectures on Wavelets
• A wavelet-Galerkin scheme for analysis of large-scale problems on simple domains
• Reproducing kernel hierarchical partition of unity, Part I?formulation and theory
• Element‐free Galerkin methods
• Introduction to wavelets in engineering
• Wavelet–Galerkin solutions for one‐dimensional partial differential equations
• Hat interpolation wavelet-based multi-scale Galerkin method for thin-walled box beam analysis
• Wavelets
• Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domains
• Numerical simulations of strain localization in inelastic solids using mesh-free methods
• Wavelet and multiple scale reproducing kernel methods
• Reproducing kernel particle methods for structural dynamics
• A wavelet-like Galerkin method for numerical solution of variational inequalities arising in elastoplasticity
• An adaptive wavelet-Galerkin method for an elastic-plastic-damage constitutive model: 1D problem

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