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Imposing Dirichlet boundary conditions directly for FFT-based computational micromechanics. [PDF]

Comput Mech
Risthaus L, Schneider M.
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Optimal Equivalent Preconditioners

SIAM Journal on Numerical Analysis, 1993
Preconditioning strategies for elliptic partial differential operators and their discrete counterparts are compared by a model problem. The technique uses a selfadjoint positive definite operator \(B\) as the preconditioner for the nonselfadjoint convection-diffusion operator \(A\). Preconditioning is done by \(A\)'s leading term plus a positive zeroth
Manteuffel, Thomas, Otto, James
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Multi-p Preconditioners

SIAM Journal on Scientific Computing, 1997
In analogy with the multigrid method, the authors present a solution method for problems based on the \(p\)-version of the finite element method whereby degrees of freedom associated with approximation order \(p\) are visited at once and separately from those of approximation order \(p-1\) and \(p+1\).
Hu, Ning, Guo, Xian-zhong, Katz, I. Norman   +2 more
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Multiresolution Approximate Inverse Preconditioners

SIAM Journal on Scientific Computing, 2001
Summary: We introduce a new preconditioner for elliptic partial differential equations (PDEs) on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second generation wavelets
Bridson, Robert, Tang, Wei-Pai
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Generalized circulant Strang‐type preconditioners

Numerical Linear Algebra with Applications, 2011
SUMMARYStrang's proposal to use a circulant preconditioner for linear systems of equations with a Hermitian positive definite Toeplitz matrix has given rise to considerable research on circulant preconditioners. This paper presents an {eiφ}‐circulant Strang‐type preconditioner. Copyright © 2011 John Wiley & Sons, Ltd.
NOSCHESE, Silvia, Lothar Reichel
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An approximate BDDC preconditioner

Numerical Linear Algebra with Applications, 2007
AbstractThe balancing domain decomposition by constraints (BDDC) preconditioner requires direct solutions of two linear systems for each substructure and one linear system for a global coarse problem. The computations and memory needed for these solutions can be prohibitive if any one system is too large.
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Circulant Preconditioners Constructed from Kernels

SIAM Journal on Numerical Analysis, 1992
The concept of a model operator as a preconditioner is one of the widely used for the solution of large elliptic grid systems. During the last decade it gained a recognition in some ``nonelliptic'' applications like the solution of systems with Toeplitz matrix \(A\) which arise, for example, in signal processing and control theory.
Chan, Raymond H., Yeung, Man-Chung
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A Multilevel AINV Preconditioner

Numerical Algorithms, 2002
An algebraic multilevel approximate inverse preconditioner, which uses the same design as the algebraic multigrid algorithm, is proposed for solving efficiently symmetric positive definite sparse linear systems in conjunction with preconditioned conjugate gradient method.
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