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- Howard C. Elman, Oliver G. Ernst, Dianne P. O'Leary
- SIAM J. Scientific Computing
- 2001

Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarseâ€¦ (More)

- Michael Eiermann, Oliver G. Ernst
- SIAM J. Numerical Analysis
- 2006

We show how the Arnoldi algorithm for approximating a function of a matrix times a vector can be restarted in a manner analogous to restarted Krylov subspace methods for solving linear systems ofâ€¦ (More)

- Oliver G. Ernst
- SIAM J. Matrix Analysis Applications
- 2000

We discuss the behavior of the minimal residual method applied to stabilized dis-cretizations of one-and two-dimensional model problems for the stationary convection-diiusion equation. In theâ€¦ (More)

- Oliver G. Ernst, ANTJE MUGLER, HANS-JÃ–RG STARKLOFF, Elisabeth Ullmann
- 2010

A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations ofâ€¦ (More)

which describes stationary reaction-diffusion phenomena but is often also called Helmholtz equation in certain communities. For example in meteorology, the early seminal papers [48, 56] led an entireâ€¦ (More)

- Michael Eiermann, Oliver G. Ernst, Stefan GÃ¼ttel
- SIAM J. Matrix Analysis Applications
- 2011

We investigate an acceleration technique for restarted Krylov subspace methods for computing the action of a function of a large sparse matrix on a vector. Its effect is to ultimately deflate aâ€¦ (More)

We present an overview of the stochastic finite element method with an emphasis on the computational tasks involved in its implementation.

- Oliver G. Ernst
- Numerical Algorithms
- 2000

An overview is given of the simplifications which arise when p-cyclic systems are solved by iterative methods. Besides the classic iterative methods, we treat the Chebyshev semi-iterative method andâ€¦ (More)

- Oliver G. Ernst
- 2007

In stochastic finite element computations for modelling uncertainty a popular approach for separating the deterministic and stochastic dependencies of a random field is to compute the first few termsâ€¦ (More)

- Elisabeth Ullmann, Howard C. Elman, Oliver G. Ernst
- SIAM J. Scientific Computing
- 2012

We consider the numerical solution of a steady-state diffusion problem where the diffusion coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of this problemâ€¦ (More)