S. Maliassov - Academia.edu (original) (raw)

Papers by S. Maliassov

Research paper thumbnail of Preconditioning Nonconforming Finite Element Approximations of Second Order Elliptic Problems

We consider the nite element approximation of the Poisson equation in a parallelepiped using line... more We consider the nite element approximation of the Poisson equation in a parallelepiped using linear tetrahedral nonconforming Crouzeix-Raviart elements. Using the idea of substructuring we eliminate most of the unknowns and precondition the obtained Schur complement by a spectrally equivalent very sparse matrix. The numerical experiments show that this solution procedure is very e cient, robust and is a good preconditioner for approximations of general elliptic equations of second order on domains, topologically equivalent to a parallelepiped.

Research paper thumbnail of Substructure Preconditioning For Porous Flow Problems

... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-emati... more ... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-ematics, Texas A&M University, College Station, TX 77843. ... where c is a constant dependent only on and where kk0; and kk2; are the L2( ) and H2( ) Sobolev norms, respectively de ned by ...

Research paper thumbnail of Substructuring Preconditioning For Finite Element Approximations Of Second Order Elliptic Problems. I. Nonconforming Linear Elements For The Poisson Equation In A Parallelepiped

Research paper thumbnail of Mathematical modeling and numerical algorithms for poroelastic problems

Contemporary Mathematics, 2003

ABSTRACT A new efficient solver with a spectrally equivalent and optimal order of computational c... more ABSTRACT A new efficient solver with a spectrally equivalent and optimal order of computational complexity preconditioner is proposed and investigated for a coupled system of differential equations resulting from the implicit time-discretization of a poroelastic problem. The diffusion part of the problem is discretized on logically structured tetrahedral grids with a mixed and mixed-hybrid finite element method. Results of numerical experiments are presented.

Research paper thumbnail of Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

Numerical Linear Algebra with Applications, 1996

A new approach for constructing algebraic multilevel preconditioners for mixed nite element metho... more A new approach for constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed. The linear system arising from the mixed methods is rst algebraically condensed to a symmetric, positive de nite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming nite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed nite element methods are presented to illustrate the present theory.

Research paper thumbnail of Substructure preconditioning for porous flow problems

... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-emati... more ... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-ematics, Texas A&M University, College Station, TX 77843. ... where c is a constant dependent only on and where kk0; and kk2; are the L2( ) and H2( ) Sobolev norms, respectively de ned by ...

Research paper thumbnail of Preconditioning of nonconforming finite element approximations of second order elliptic problems

... Approximations of Second Order Elliptic Problems RE Ewing, Y. Kuznetsov,y RD Lazarov, and S. ... more ... Approximations of Second Order Elliptic Problems RE Ewing, Y. Kuznetsov,y RD Lazarov, and S. Maliassov ... Note, that all unknowns on faces on the boundary with Dirichlet data are excluded. Let (u;v) and kvk be a bilinear form and the corresponding norm, de ned on RN by ...

Research paper thumbnail of Substructuring preconditioning for finite element approximations of second order elliptic problems. I. Nonconforming linear elements for the Poisson equation in parallelepiped

Research paper thumbnail of General Parallel Reservoir Simulation

Abu Dhabi International Petroleum Exhibition and Conference, 2015

Research paper thumbnail of Parallel Reservoir Simulation Using a Specific Software Framework

SPE Reservoir Simulation Symposium, 2013

Research paper thumbnail of On the Schwarz alternating method for eigenvalue problems

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of The family of nested factorizations

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of Homogenized mixed finite element method for diffusion equations on prismatic meshes

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of Substructuring preconditioners for nonconforming finite element approximations of second-order elliptic problems with anisotropy

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of SparSol: sparse linear systems solver

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

ABSTRACT SparSol is a software package intended for the preconditioned iterative solution of larg... more ABSTRACT SparSol is a software package intended for the preconditioned iterative solution of large sparse linear systems. It includes sets of iterative method s, preconditioners, scaling and reordering algorithms that allows to choose the optimal combination of algorithms for a particular problem. The paper briefly describes the algorithms implemented and nume rically compares the performance of SparSol with that of several popular, freely available software pac kages using test systems arising from hydrocarbon reservoir simulations.

Research paper thumbnail of Preconditioning Nonconforming Finite Element Approximations of Second Order Elliptic Problems

We consider the nite element approximation of the Poisson equation in a parallelepiped using line... more We consider the nite element approximation of the Poisson equation in a parallelepiped using linear tetrahedral nonconforming Crouzeix-Raviart elements. Using the idea of substructuring we eliminate most of the unknowns and precondition the obtained Schur complement by a spectrally equivalent very sparse matrix. The numerical experiments show that this solution procedure is very e cient, robust and is a good preconditioner for approximations of general elliptic equations of second order on domains, topologically equivalent to a parallelepiped.

Research paper thumbnail of Substructure Preconditioning For Porous Flow Problems

... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-emati... more ... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-ematics, Texas A&M University, College Station, TX 77843. ... where c is a constant dependent only on and where kk0; and kk2; are the L2( ) and H2( ) Sobolev norms, respectively de ned by ...

Research paper thumbnail of Substructuring Preconditioning For Finite Element Approximations Of Second Order Elliptic Problems. I. Nonconforming Linear Elements For The Poisson Equation In A Parallelepiped

Research paper thumbnail of Mathematical modeling and numerical algorithms for poroelastic problems

Contemporary Mathematics, 2003

ABSTRACT A new efficient solver with a spectrally equivalent and optimal order of computational c... more ABSTRACT A new efficient solver with a spectrally equivalent and optimal order of computational complexity preconditioner is proposed and investigated for a coupled system of differential equations resulting from the implicit time-discretization of a poroelastic problem. The diffusion part of the problem is discretized on logically structured tetrahedral grids with a mixed and mixed-hybrid finite element method. Results of numerical experiments are presented.

Research paper thumbnail of Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

Numerical Linear Algebra with Applications, 1996

A new approach for constructing algebraic multilevel preconditioners for mixed nite element metho... more A new approach for constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed. The linear system arising from the mixed methods is rst algebraically condensed to a symmetric, positive de nite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming nite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed nite element methods are presented to illustrate the present theory.

Research paper thumbnail of Substructure preconditioning for porous flow problems

... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-emati... more ... Ewing, R. Lazarov, S. Maliassov, Istitute for Scienti c Computation, Department of Math-ematics, Texas A&M University, College Station, TX 77843. ... where c is a constant dependent only on and where kk0; and kk2; are the L2( ) and H2( ) Sobolev norms, respectively de ned by ...

Research paper thumbnail of Preconditioning of nonconforming finite element approximations of second order elliptic problems

... Approximations of Second Order Elliptic Problems RE Ewing, Y. Kuznetsov,y RD Lazarov, and S. ... more ... Approximations of Second Order Elliptic Problems RE Ewing, Y. Kuznetsov,y RD Lazarov, and S. Maliassov ... Note, that all unknowns on faces on the boundary with Dirichlet data are excluded. Let (u;v) and kvk be a bilinear form and the corresponding norm, de ned on RN by ...

Research paper thumbnail of Substructuring preconditioning for finite element approximations of second order elliptic problems. I. Nonconforming linear elements for the Poisson equation in parallelepiped

Research paper thumbnail of General Parallel Reservoir Simulation

Abu Dhabi International Petroleum Exhibition and Conference, 2015

Research paper thumbnail of Parallel Reservoir Simulation Using a Specific Software Framework

SPE Reservoir Simulation Symposium, 2013

Research paper thumbnail of On the Schwarz alternating method for eigenvalue problems

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of The family of nested factorizations

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of Homogenized mixed finite element method for diffusion equations on prismatic meshes

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of Substructuring preconditioners for nonconforming finite element approximations of second-order elliptic problems with anisotropy

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

Research paper thumbnail of SparSol: sparse linear systems solver

Russian Journal of Numerical Analysis and Mathematical Modelling, 2000

ABSTRACT SparSol is a software package intended for the preconditioned iterative solution of larg... more ABSTRACT SparSol is a software package intended for the preconditioned iterative solution of large sparse linear systems. It includes sets of iterative method s, preconditioners, scaling and reordering algorithms that allows to choose the optimal combination of algorithms for a particular problem. The paper briefly describes the algorithms implemented and nume rically compares the performance of SparSol with that of several popular, freely available software pac kages using test systems arising from hydrocarbon reservoir simulations.