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 Kent Andre Mardal

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Average citations per article9.77
Citation Count127
Publication count13
Publication years2002-2013
Available for download1
Average downloads per article415.00
Downloads (cumulative)415
Downloads (12 Months)23
Downloads (6 Weeks)3
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March 2013 Numerische Mathematik: Volume 123 Issue 3, March 2013
Publisher: Springer-Verlag New York, Inc.
Citation Count: 0

We construct a new Fortin operator for the lowest order Taylor---Hood element, which is uniformly stable both in $$L^2$$ and $$H^1$$ . The construction, which is restricted to two space dimensions, is based on a tight connection between a subspace of the Taylor---Hood velocity space and the lowest order Nedelec ...
Keywords: 65N22, 65N30

February 2012
Citation Count: 73

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available ...

October 2010 SIAM Journal on Control and Optimization: Volume 48 Issue 8, September 2010
Publisher: Society for Industrial and Applied Mathematics
Citation Count: 0

This paper is devoted to the numerical treatment of linear optimality systems (OS) that arise in connection with inverse problems for partial differential equations. If such inverse problems are regularized by Tikhonov regularization, then it follows from standard theory that the associated OS is well-posed, provided that the regularization parameter ...
Keywords: all-at-once methods, optimality systems, preconditioning, Tikhonov regularization, electrocardiography, minimal residual method, inverse problems, isolated eigenvalues

4 published by ACM
January 2010 ACM Transactions on Mathematical Software (TOMS): Volume 37 Issue 1, January 2010
Publisher: ACM
Citation Count: 5
Downloads (6 Weeks): 3,   Downloads (12 Months): 23,   Downloads (Overall): 415

Full text available: PDFPDF
Efficient and easy implementation of variational forms for finite element discretization can be accomplished with metaprogramming. Using a high-level language like Python and symbolic mathematics makes an abstract problem definition possible, but the use of a low-level compiled language is vital for run-time efficiency. By generating low-level C++ code based ...
Keywords: code generation, Variational forms, automation, finite element, compiler, metaprogramming

November 2009 International Journal of Computational Science and Engineering: Volume 4 Issue 4, November 2009
Publisher: Inderscience Publishers
Citation Count: 7

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, ...

May 2007 Computing in Science and Engineering: Volume 9 Issue 3, May 2007
Publisher: IEEE Educational Activities Department
Citation Count: 1

This article describes two Python modules for solving partial differential equations (PDEs): PyCC is designed as a Matlab-likeenvironment for writing algorithms for solving PDEs, and SyFi creates matrices based on symbolic mathematics, code generation, and thefinite element method.
Keywords: PDEs, Python, computer languages, simulations, PDEs, Python, computer languages, simulations

January 2007 SIAM Journal on Scientific Computing: Volume 29 Issue 1, January 2007
Publisher: Society for Industrial and Applied Mathematics
Citation Count: 2

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank-Nicolson schemes can be reused for higher-order fully implicit Runge-Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order-optimal for A-stable and irreducible Runge-Kutta schemes with invertible coefficient matrices. The ...
Keywords: Runge-Kutta schemes, parabolic PDE, preconditioners

June 2006 PARA'06: Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Publisher: Springer-Verlag
Citation Count: 0

SyFi is an open source C++ library for defining and using variational forms and finite elements based on symbolic representations of polygonal domains, degrees of freedom and polynomial spaces. Once the finite elements and variational forms are defined, they are used to generate efficient C/C++ code.

March 2006 Numerische Mathematik: Volume 103 Issue 1, March 2006
Publisher: Springer-Verlag New York, Inc.
Citation Count: 0

March 2006 Numerische Mathematik: Volume 103 Issue 1, March 2006
Publisher: Springer-Verlag New York, Inc.
Citation Count: 2

August 2004 Numerische Mathematik: Volume 98 Issue 2, August 2004
Publisher: Springer-Verlag New York, Inc.
Citation Count: 12

Implicit time stepping procedures for the time dependent Stokes problem lead to stationary singular perturbation problems at each time step. These singular perturbation problems are systems of saddle point type, which formally approach a mixed formulation of the Poisson equation as the time step tends to zero. Preconditioners for discrete ...

May 2002 SIAM Journal on Numerical Analysis: Volume 40 Issue 5, 2002
Publisher: Society for Industrial and Applied Mathematics
Citation Count: 23

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. ...
Keywords: nonconforming finite elements, singular perturbation problems, uniform error estimates, Darcy--Stokes flow

April 2002 ICCS '02: Proceedings of the International Conference on Computational Science-Part III
Publisher: Springer-Verlag
Citation Count: 0

Many code developers think the implementation of mixed finite elements on general unstructured meshes is challenging. This assertion is reflected in the many efforts on constructing stabilized finite element methods (e.g. for flow problems), where standard elements can be used, and the fact that there are very few libraries offering ...

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