Currently displaying 1 – 10 of 10

Showing per page

Order by Relevance | Title | Year of publication

Some practical aspects of parallel adaptive BDDC method

Šístek, JakubMandel, JanSousedík, Bedřich — 2012

Applications of Mathematics 2012

We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may...

A convergent nonlinear splitting via orthogonal projection

Jan Mandel — 1984

Aplikace matematiky

We study the convergence of the iterations in a Hilbert space V , x k + 1 = W ( P ) x k , W ( P ) z = w = T ( P w + ( I - P ) z ) , where T maps V into itself and P is a linear projection operator. The iterations converge to the unique fixed point of T , if the operator W ( P ) is continuous and the Lipschitz constant ( I - P ) W ( P ) < 1 . If an operator W ( P 1 ) satisfies these assumptions and P 2 is an orthogonal projection such that P 1 P 2 = P 2 P 1 = P 1 , then the operator W ( P 2 ) is defined and continuous in V and satisfies ( I - P 2 ) W ( P 2 ) ( I - P 1 ) W ( P 1 ) .

Model analysis of BPX preconditioner based on smoothed aggregation

Pavla FraňkováJan MandelPetr Vaněk — 2015

Applications of Mathematics

We prove nearly uniform convergence bounds for the BPX preconditioner based on smoothed aggregation under the assumption that the mesh is regular. The analysis is based on the fact that under the assumption of regular geometry, the coarse-space basis functions form a system of macroelements. This property tends to be satisfied by the smoothed aggregation bases formed for unstructured meshes.

On the convergence of the ensemble Kalman filter

Jan MandelLoren CobbJonathan D. Beezley — 2011

Applications of Mathematics

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and L p bounds on the ensemble then give L p convergence.

Page 1

Download Results (CSV)