Consider applying the Conjugate Residual (CR) method, which is a Krylov subspace type iterative solver, to systems of linear equations Ax = b or least squares problems min x∈Rn ‖b −Ax‖2, where A is singular and nonsymmetric. We will show that when R(A)⊥ = kerA, the CR method can be decomposed into the R(A) and kerA components, and the necessary and sufficient condition for the CR method to conv...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

The complex variable boundary element method, CVBEM, employs the Cauchy integral with any complex variable (e.g., complex potential, complex flux, or complex velocity) to solve boundary value problems. The CVBEM formulation is consistent with the primal and dual solutions of the boundary integral equation, as well as the analytic element method. The resulting problem is overdetermined because t...

and Kk(BA,Br) = span{Br, (BA)Br, . . . , (BA)k−1Br}, (3) where B ∈ Rn×m is the mapping and preconditioning matrix, and apply Krylov subspace iteration methods on these subspaces. For overdetermined problems, applying the standard CG method to Kk(BA,Br) leads to the preconditioned CGLS [3] or CGNR [9] method while for underdetermined problems it leads to preconditioned CGNE [9] method. The GMRES...

Article history: Received 16 July 2016 Received in revised form 30 January 2017 Accepted 8 February 2017 Available online 14 February 2017

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via moving least squares (MLS) method. The resulting kernels effectively couple structural degrees of freedom to fluid variables on only one side the fluid-structure interface. reduces spurious feedback forcing and internal flows that are typically observed in IB models use isotropic structure both ...