**Cornelis W. Oosterlee**
### Reports and Publications, sorted

## PDEs Discretization

`Analysis of an affine version of the Heston-Hull-White option pricing partial differential equation.'
(with S.Guo, Lech Grzelak) 2013.
`An ENO-based numerical Method for Second-Order Equations and Application to the Control of Dike Levels.'
(with S.P. van der Pijl) J. Sci. Comput. 2012.
## Multigrid Development

### Poro-Elasticity Equations (with Francisco Gaspar et al.)

'A simple and efficient segregated smoother for the discrete Stokes equations' (with F.J. Gaspar, Y. Notay and C. Rodrigo. Submitted for publication.

`Distributive Smoothers in Multigrid for Problems with Dominating Grad-Div Operators.' (with F.J. Gaspar, J.L. Gracia, F.J. Lisbona, P.N. Vabishchevich). Num. Lin. Algebra Appl. 15: 661-683 (2008).

`An Efficient Multigrid Solver for a Reformulated Version of the Poroelasticity System.' (with F.J. Gaspar, F.J. Lisbona, P.N. Vabishchevich). Computer Meth. Applied Mech. Engineering, 196: 1447-1457 (2007).

`An efficient multigrid solver based on distributive smoothing for poroelasticity equations.' (with R. Wienands, F.J. Gaspar, F.J. Lisbona)

Computing 73, 99-119 (2004).

`A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity system.' (with F.J. Gaspar, F.J. Lisbona, R. Wienands), Num. Lin. Algebra Appl. 11, 93-113 (2004).

### Helmholtz Equation (with Yogi Erlangga et al.)

`A multigrid-based shifted-Laplacian preconditioner for a fourth order Helmholtz discretization.' (with N. Umetani, S.P. MacLachlan), Num. Lin. Algebra Appl. 16: 603-626 (2009).

`A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems.' (with Y.A. Erlangga, C. Vuik), SIAM J. Sci. Comput. 27: 1471-1492 (2006).

`Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation.' (with Y.A. Erlangga, C. Vuik), Applied Num. Math. 56: 648-666 (2006).

`On a class of preconditioners for solving the Helmholtz equation.' (with Y.A. Erlangga, C. Vuik), Applied Num. Math. 50, 409-425 (2004).

### Local Fourier Analysis for Multigrid (with Roman, Scott, Francisco, Carmen, Irad)

`Accuracy measures and Fourier analysis for the full multigrid algorithm.' (with C. Rodrigo, F.J. Gaspar and I. Yavneh), to appear in SIAM J. Scient. Comp.

`Local Fourier analysis for multigrid with overlapping smoothers applied to systems of PDEs.' (with S.P. MacLachlan), to appear in Num. Lin. Algebra Applications.

`A genetic search for optimal multigrid components within a Fourier analysis setting.' (with R. Wienands), SIAM J. Scient. Comp. 24, 924-944 (2002).

`On three-grid Fourier analysis for multigrid' (with R. Wienands), SIAM J. Scient. Comp. 23, 651-671 (2001).
`Fourier analysis of GMRES(m) preconditioned by multigrid.' (with R. Wienands, T. Washio) SIAM J. Scient. Comp. 22, 582-603 (2000).

### Multigrid Algorithm Development (with Hisham, Scott, Takumi, Francisco, Jari)

`A projected algebraic multigrid method for linear complementarity problems' (with J. Toivanen), Num. Math. Theor. Meth. Applic. 2012.

`Algebraic multigrid solvers for complex-valued matrices' (with S.P. MacLachlan), SIAM J. Sci. Comput. 30: 1548-1571 (2008).

`Efficient D-Multigrid preconditioners for sparse-grid solution of high dimensional partial differential equations on non-equidistant grid' (with H. bin Zubair), Int. J. Comp. Math., 8: 1129-1147 (2007).

`Multigrid for high dimensional elliptic partial differential equations on non-equidistant grid' (with H. bin Zubair, R. Wienands), SIAM J. Sci. Comput. 29: 1613-1636 (2007).

`Geometric multigrid with applications to computational fluid dynamics.' (with P. Wesseling) J. Comp. Appl. Math. 128, 311-334 (2001).

`Error analysis for a potential problem on locally refined grids.' (with T. Washio), Numer. Math. 86, 539-563 (2000).

`Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows.' (with T. Washio), SIAM J. Scient. Comp. 21, 1670-1690 (2000).

`Flexible multiple semicoarsening for three dimensional singularly perturbed problems.' (with T. Washio), SIAM J. Scient. Comp. 19, 1646-1666 (1998).

`Multigrid line smoothers for higher order upwind discretizations of convection-dominated problems.' (with F.J. Gaspar, T. Washio and R. Wienands) J. Comp. Physics 139, 274-307 (1998).

`An evaluation of parallel multigrid as a solver and as a preconditioner for singularly perturbed problems.'(with T. Washio) SIAM J. Scient. Comp. 19, 87-110 (1998).

`Krylov subspace acceleration for nonlinear multigrid schemes.' (with T. Washio) Electr. Trans. on Num. Analysis, 6, 271-290 (1997).

`A GMRES-based plane smoother in multigrid to solve 3D anisotropic fluid flow problems.' J. Comp. Physics 130, 41-53 (1997).