email:p.oswald@jacobs-university.de
office:
Jacobs University Bremen
Research I, Room 113
600 Campus Ring 1
28759
Bremen
Germany
Phone: ++49-421-200-3179
Fax:
++49-421-200-3103
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| Education |
- Diploma, Mathematics, Odessa State University
(Ukraine/Soviet Union), 1975
- Ph.D. 1 (Promotion, Dr.rer.nat.), Mathematics, Moscow
Institute of Electronical Engineering (Russia/Soviet Union),
1978
- Ph.D. 2 (Habilitation, Dr.habil.), Mathematics, University
of Jena (Germany), 1982
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| Research Interests |
- Approximation Theory and Algorithms
- Function Spaces and Applied Harmonic Analysis
- Multiscale Methods in Scientific Computing
- Numerical Methods for PDEs
- Finite Elements, Splines, Wavelets
- Mathematical Modelling
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| Selected publications
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- P. Oswald, Multilevel Finite Element Approximation:
Theory and Applications. Teubner Skripte zur Numerik,
Teubner, Stuttgart, 1994 (ISBN 3-519-02719-4)
- P. Oswald, Stable subspace splittings for Sobolev
spaces and some domain decomposition algorithms. In:
Proc. 7th Symp. on Domain Decomposition Methods, Penn State
Univ. 1993 (D.Keyes, J.Xu, eds.), Contemporary Math. vol.
180, AMS, Providence 1994, pp. 87-98.
- P. Oswald, Preconditioners
for nonconforming elements. Math. Comp. 65
(1996) 923-941.
- P. Oswald, Intergrid
transfer operators and multilevel preconditioners for
nonconforming discretizations. Appl. Numer. Math.
23 (1996) 139-158.
- P. Oswald, An
optimal multilevel preconditioner for solenoidal
approximations of the 2D-Stokes problem. IMA J.
Numer. Anal. 14 (1997) 1-22.
- P. Oswald, On
the robustness of the BPX-preconditioner with respect to
jumps in the coefficients. Math. Comp. 68
(1999) 633-650.
- Z. Chen, P. Oswald, Multigrid
and multilevel methods for nonconfoming rotated Q1-elements.
Math. Comp. 67 (1998) 667-693.
- P. Oswald, Multilevel
solvers for elliptic problems on domains. In:
Multiscale Wavelet Methods for PDEs, W.Dahmen, A.Kurdila,
P.Oswald (eds.), Academic Press, 1997, 3-58.
- J. Ko, A. Kurdila, P. Oswald, Scaling
function and wavelet preconditioners for second order
ellliptic problems. In: Multiscale Wavelet Methods
for PDEs, W.Dahmen, A.Kurdila, P.Oswald (eds.), Academic
Press, 1997, 413-438.
- R. Lorentz, P. Oswald, Multilevel
finite element Riesz bases for Sobolev spaces. In:
Proc. 9th Intern. Conf. on Domain Decomposition Methods in
Science and Engineering (P. Bjorstad et al., eds.), Domain
Decomposition Press, Bergen, 1998, pp. 178-187.
- R. Lorentz, P. Oswald, Nonexistence
of compactly supported box spline prewavelets in Sobolev
spaces. In: Curves and Surfaces, Proceedings of
Chamonix 1996 (A. Le Mehaute, C. Rabut, L.L. Schumaker,
eds.), Vanderbilt Univ. Press, Nashville, 1997, pp.
235--244.
- R. Lorentz, P. Oswald, Criteria
for hierarchical bases for Sobolev spaces. Appl.
Comput. Harm. Anal. 8 (2000), 32-85 (see also:
GMD-Arbeitspapiere Nr. 1059, March 1997).
- P. Oswald, On
norm bounds for iterated intergrid transfer operators.
GMD-Arbeitspapiere Nr. 1079, June 1997.
- P. Oswald, Multilevel
norms for H-1/2. Computing 61
(1998), 235-255.
- P. Oswald, Multigrid
prolongations and matrix subdivision. In:
Approximation Theory IX, vol. 2 (C.K. Chui, L.L. Schumaker,
eds.), Vanderbilt Univ. Press, Nashville, 1998, pp. 275-283.
- M. Griebel, P. Oswald, T. Schiekofer Sparse
grids for boundary integral equations. Numer. Math.
83 (1999), 279-312.
- P. Oswald, Subspace
correction methods and multigrid theory. Guest
contribution in: U. Trottenberg, C. W. Oosterlee, A.
Schüller, Multigrid, Acad. Press, San Diego, 2001, pp.
533-572.
- P. Oswald, On
best N-term approximation by Haar functions in
Hs-norms. In: Metric Function Theory and
Related Topics in Analysis (S. M. Nikolskij, B. S. Kashin,
A. D. Izaak, eds.), AFC, Moscow, 1999, pp. 137-163
(translated into Russian).
- P. Oswald, Interface
preconditioners and multilevel extension operators.
In: Proc. 11th Intern. Conf. on Domain Decomposition Methods
in Science and Engineering (C.-H. Lai et al., eds.), London,
1998, published by ddm.org, 1999, pp. 96-103.
- P. Oswald, Best
N-term capacitance approximation on sparse grids.
Proc. 12th Intern. Conf. on Domain Decomposition Methods in
Science and Engineering (T. Chan et al., eds.), Chiba, 1999,
published by ddm.org, 2001, pp. 437-444.
- P. Oswald, Remarks
on multilevel bases for divergence-free finite
elements. Numerical Algorithms 27, 2001, 131-152.
- P. Oswald, Greedy
algorithms and best m-term approximation with respect to
biorthogonal systems. J. Fourier Anal. Appl. 7, 4,
2001, 325-341.
- P. Oswald, B. Wohlmuth, On
polynomial reproduction of dual FE bases. 13th
Intern. Conf. on Domain Decomposition Methods in Science and
Engineering (N. Debit et al., eds.), Lyon, 2000, published
by ddm.org 2001, 85--96.
- P. Oswald, Extremal
properties of trigonometric polynomials with applications to
signal design. Int. Conf. Trends in Approximation
Theory (K. Kopotun, T. Lyche, M. Neamtu, eds.), Vanderbilt
Univ. Press, Nashville, 2001, pp. 343-352.
- P. Oswald, M. A. Shokrollahi, Capacity-achieving
sequences for the erasure channel. IEEE Trans. on
Information Theory, 48, 12, Dec. 2002, 3017-3028 (
short version presented at ISIT 2001, preprint
version ). Supporting Matlab
routines are available online.
- Q. Jiang, P. Oswald, Triangular
sqrt(3)-subdivision schemes: the regular case. J.
Comput. Appl. Math. 156, 2003, 47--75. For a preprint
version with all figures included, click here
, supporting Matlab
routines are available online.
- Q. Jiang, P. Oswald, S. Riemenschneider sqrt(3)-subdivision
schemes: maximal sum rule orders Constr. Approx. 19,
3, 2003, 437-463.
- P. Oswald, P. Schroeder Composite
primal/dual sqrt(3)-subdivision schemes CAGD 20, 3,
2003, 135--164
- P. Oswald Smoothness
of nonlinear median-interpolation subdivision Adv.
Comput. Math. 20, 2004, 401--423.
- P. Oswald Smoothness
of a nonlinear subdivision scheme in Curves and
Surface Fitting: Saint-Malo 2002, A. Cohen, J.-L. Merrien,
L. L. Schumaker (eds.), Nashboro Press, Brentwood, 2003, pp.
323-332 (for an extended version, click here
).
- C. K. Madsen, P. Oswald Optical
filter architecture for approximating any 2 x 2 unitary
matrix Optics Letters, vol. 28, no. 7, Apr. 2003,
534-536.
- P. Oswald, C. K. Madsen, R. L. Konsbruck
Analysis of scalable PMD compensators using FIR filters and
wavelength-dependent optical power measurements
J. Lightwave Technol., vol. 22, no. 2, Feb. 2004, 647-657.
- C. K. Madsen, P. Oswald, M. Capuzzo, E. Chen, L. Gomez, A. Griffin,
A. Kasper, E. Laskowski, L.Stulz, A. Wong-Foy, Reset-free integrated
polarization controller using phase shifters
IEEE J. Sel. Topics in Quantum Electronics, vol. 11, no. 2, March/April 2005,
431-438.
- P. Oswald,
Designing composite triangular subdivision schemes
CAGD 22 (2005), 659-679 (click here
for an extended version).
- M. Griebel, P. Oswald, M. A. Schweitzer,
A particle-partition of unity method-Part VI: A p-robust multilevel solver
In Meshfree Methods for Partial Differential Equations II
(M. Griebel and M. A. Schweitzer, editors), Lecture Notes in Computational
Science and Engineering vol. 43, pages 71-92. Springer, 2005.
- P. Oswald, C. K. Madsen
Deterministic analysis of endless tuning of polarization
controllers
J. Lightwave Technol., vol. 24, no. 7, July 2006, 2932-2939.
- P. Oswald
Semiorthogonal linear prewavelets
on irregular meshesIn Approximation and Probability,
Banach Center Publ. vol. 72,
Inst. Math. Polish Acad. Sci., 2006, 221-234.
- P. Oswald A counterexample for
the L2-projector onto linear spline
spacesMathematics of Computation, 77, 2008, 221-226.
- P. Oswald, T. Shingel
Splitting methods for
SU(N) loop approximation J. Approx. Th. 161(1), 2009, 174-186.
- P. Oswald
Optimality of multilevel preconditioning for nonconforming P1 finite elements
Numerische Mathematik, 111, 2, 2008, 267-291.
- J. Maes, P. Oswald
Multilevel finite element preconditioning for sqrt(3) refinement
Mathematics of Computation, 78, 268, 2009, 1869-1890.
- S. Harizanov, P. Oswald
Stability of nonlinear subdivision and multiscale transforms
Constr. Approx. 2008 (accepted).
- P. Oswald, T. Shingel
Close-to-optimal bounds for SU(N) loop approximation J. Approx. Th. 2008 (submitted).
- N. Dyn, P. Oswald
Univariate subdivision and multiscale transforms: The nonlinear case
in Multiscale, Nonlinear, and Adaptive Approximation (R.A. DeVore, A. Kunoth eds.),
pp. 203-247, Springer, Berlin, 2009.
- P. Oswald
Stable space splittings and fusion frames in Wavelets XIII
(V.K. Goyal, M. Papadakis, D. Van de Ville, eds.), Proc. SPIE Vol. 7446
(SPIE, Bellingham, 2009), 744611. doi:10.117/12.825303
- S. Harizanov, P. Oswald, T. Shingel
Normal multi-scale transforms for curves Found. Comput. Math. 2009 (submitted).
- Reading materials for survey lectures on
multilevel schemes for elliptic problems in Sobolev spaces
(originally given in 1997-98 in various places) are also available:
Frames and space splittings in Hilbert spaces ,
Multilevel frames and Riesz bases in Sobolev spaces ,
Multilevel ... .
- For further references, see my list
of publications. My CV can be downloaded here.
- Matlab routines for some of my papers can be found here
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