In this work we discuss parallel preconditioning techniques for the bidomain equations, a non-linear system of partial differential equations which is widely used for describing electrical activity in cardiac tissue. We focus on the solution of the linear system associated with the elliptic part of the bidomain model, since it dominates computation, with the preconditioned conjugate gradient me...

This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An e...

We study the preconditioning of the stiffness matrix which arises from the discretization of the Poisson equation using IsoGeometric Method (IGM). A study of condition number of stiffness matrices, resulting from NURBS based IGM, suggests that novel preconditioning techniques are needed for fast and efficient iterative solvers for the resulting linear system. As a first step towards preconditio...

We develop a class of parallel multistep successive preconditioning strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques. The key idea is to compute a series of simple sparse matrices to approximate the inverse of the original matrix. Studies are conducted to show the advantages of such an approach in terms of both improving precondit...

Standard preconditioners, such as ILU factorizations, often break down in construction for KKT matrices. We compare several approaches for preconditioning KKT systems. The first applies a constraint preconditioner by incorporating robust factored approximations of (BB ) and BB , where B is the (2,1) block of the KKT matrix. In the second approach, we apply permutations and scalings that maximiz...

This paper presents a few preconditioning techniques for solving general sparse linear systems on distributed memory environments. These techniques utilize the Schur complement system for deriving the preconditioning matrix in a number of ways. Two of these pre-conditioners consist of an approximate solution process for the global system, which exploit approximate LU factorizations for diagonal...

The present study has investigated the effectiveness of staged-preconditioning, in both remote and target organs. After IP the myocardial release of the biochemical markers including, creatine phosphokinase (CPK), cardiac creatine kinase (CK-MB), cardiac troponin T (cTnT) and lactate dehydrogenase (LDH) were evaluated in patients who underwent CABG, with and without staged-preconditioning. Sixt...

This review focuses on the genomic response following a preconditioning stimulus. Initial studies demonstrated that classical ischemic preconditioning mediated by cyclic episodes of short durations of reversible ischemia and reperfusion could result in the reprogramming of gene expression. Some of these genes are translated into proteins during the late preconditioning or so-called "second wind...