Nicolas Robidoux's home page (in need of a serious update)
I was also one of the organizers of the NSF funded
Personal information
Refereed publications
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Computer algebra and interpolation: a lesson plan, Journal
of Symbolic Computation (1997) 23, 551-576.
BibTeX entry (1K).
The following short and elementary proceedings article is
recommended as an introduction to natural (mimetic) discretization
methods for div-grad systems. My doctoral thesis (see below), which
is more technical and comprehensive, is a continuation of this work.
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A new method of construction of adjoint gradients and
divergences on logically rectangular smooth grids, 261-272 in
Finite Volumes for Complex Applications, F. Benkhaldoun
and R. Vilsmeier, editors (Hermes, Paris, 1996).
Abstract.
Abstract in French (minus the accents).
Postscript file rouen.ps (200K).
Gziped Postscript file rouen.ps.gz (70K).
BibTeX entry (1K).
With Adrian Kitson and Robert
I. McLachlan:
-
Skew-adjoint finite difference methods, accepted for
publication in the New Zealand Journal of Mathematics.
With Patrick M. Knupp:
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A framework for variational grid generation: conditioning the
Jacobian matrix with matrix norms, Society for Industrial and
Applied Mathematics Journal on Scientific Computing 21 (2000),
no. 6, 2029-2047.
Summary (Mathematical Reviews 2002a:65148).
The article.
BibTeX entry (1K).
With Robert
I. McLachlan:
-
Antisymmetry, pseudospectral methods, and conservative PDEs,
in International Conference on Differential Equations,
Proceedings of the conference (Equadiff 99) held in Berlin, August
1-7, 1999, B. Fiedler, K. Groger and J. Sprekels, editors
(World Scientific, Singapore, 2000), vol. 2, 994-999.
MathScinet listing.
Abstract.
Postscript file skew.ps (200K).
Gziped Postscript file skew.ps.gz (70K).
BibTeX entry (1K).
With Robert
I. McLachlan and
G. Reinout W. Quispel:
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Geometric integration using discrete gradients, Royal
Society of London Philosophical Transactions, Series A,
Mathematical, Physical and Engineering Sciences (1999) 357,
no. 1754, 1021-1046.
Steve Shkoller's review/summary (Mathematical Reviews
2000f:34021).
BibTeX entry (1K).
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Unified approach to Hamiltonian systems, Poisson systems,
gradient systems, and systems with Lyapunov functions or first
integrals, Physical Review Letters (1998) 12, 2399-2403.
Summary (Mathematical Reviews 99f:58079).
The article.
BibTeX entry (1K).
Selected other publications
Downloadable preprints
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Preprint of A discrete calculus in tensor grids by Stanly Steinberg and
yours truly. This paper is meant to be fairly elementary. In
fairly good shape although some proofs need to be redone. (59
pages.)
Postscript
file discrete_intro.ps (600K).
Gziped Postscript file discrete_intro.ps.gz (200K).
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Preprint of Polynomial histopolation, superconvergent degrees
of freedom, and pseudospectral discrete Hodge operators by
yours truly. I like this paper a lot. The most important
consequence of the material presented in this paper is that
discrete Hodge stars from fluxes to circulations (based on face
elements) and discrete Hodge star operators from masses to point
values (based on histopolation) can be made superconvergent
simultaneously when using hexahedral master elements. In need of a
complete rewrite. (33 pages.)
Postscript file histogram.ps (800K).
Gziped Postscript file histogram.ps.gz (300K).
PDF file histogram.pdf (500K).
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Preprint of Antisymmetry, pseudospectral methods, weighted
residual discretizations, and energy conserving partial
differential equations by Robert McLachlan
and yours truly.
Covers a lot of ground. The link to mixed Finite Element Methods
needs to be made explicit, and the writing needs to be tightened
up (there are some minor inconsistencies in the exposition). Read
the above Antisymmetry, pseudospectral methods, and
conservative PDEs first. (37 pages.)
Abstract.
Postscript
file skew.ps (2000K).
Gziped
Postscript file skew.ps.gz (300K).
-
Draft of my first pass at a doctoral thesis as it stood in 1997
(time of my ABD flight to the southern hemisphere) Natural
Finite Volume Discretizations of the Gradient, Divergence,
Laplacian, Diffusion Tensor and Advective Term on Grids with
Quadrilateral Cells.
Lots of numerical test results. The schemes described and tested
here coincide in 1D with the ones analysed in the final thesis
when the diffusion coefficient is constant on each cell. (83
pages.)
Abstract.
Postscript file oldthes.ps (600K).
Gziped Postscript file oldthes.ps.gz (200K).
Gziped Postscript file oldthes.bib (1K).
BibTeX entry (1K).
Current research interests
- Numerical analysis:
Mixed methods based on the generalized Stokes Theorem and discrete
constitutive relations. Discrete Hodge star
operators. Superconvergent face elements. Numerical
homogenization.
Discrete Hodge-Helmoltz decomposition. Numerical solution of div-grad
and curl-curl systems. Numerical computation of eddy
currents.
Conservative and structure preserving finite volume difference
discretizations of the diffusion operator with rough heterogeneous,
non-isotropic media (discontinuous degenerate full tensor diffusion
coefficients, unbounded and discontinuous source terms, non-smooth
grids with hexahedral cells).
Numerical solution of nonlinear parabolic equations. Block
pseudospectral solution of the diffusion equation.
Structural factorizations of numerical differential operators.
Conservative and structure preserving weighted residual, spectral,
pseudospectral and finite element discretizations of (nonlinear)
Hamiltonian (Lie-Poisson) partial differential equations.
- Grid generation:
Application of differential geometry to the variational generation of
structured grids (functionals involving the Jacobian matrix, metric
tensor, or Hessian of the induced mapping).
- Mathematical physics:
Existence of smooth factorizations of differential operators inducing
single or multiple conserved quantities and/or Lyapunov functionals.
Last major modification January 16, 2004.
Comments/inquiries:
nrobidoux@cs.laurentian.ca (Nicolas Robidoux)