A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients

作者：Bialecki Bernard; Karageorghis Andreas

来源：Numerical Algorithms, 2018, 77(2): 491-516.

DOI：10.1007/s11075-017-0325-x

• Cauchy-Navier equations
• Legendre polynomials
• Spectral methods
• Matrix decomposition algorithm
• Preconditioned conjugate gradient method

We solve the Dirichlet and mixed Dirichlet-Neumann boundary value problems for the variable coefficient Cauchy-Navier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear system is solved by the preconditioned conjugate gradient (PCG) method with a preconditioner which is shown to be spectrally equivalent to the matrix of the resulting linear system. Numerical tests demonstrating the convergence properties of the scheme and PCG are presented.

• 出版日期2018-2