IM PAN - Analiza Numeryczna

Samodzielna Pracownia Analizy Numerycznej

Kierownik:

prof. dr hab. Teresa Regińska (prof. zw.)
email
pok. 111, tel.: 22 5228 121

Pracownicy:

Doktoranci:

Przemysław Zieliński
email

O Pracowni

Research activities:

Numerical analysis of spectral problems (Pokrzywa, Regińska)
Numerical analysis of methods for solving partial differential equations (Wakulicz, Deriaz)
Applications of wavelets to problems of numerical analysis (Deriaz, Pokrzywa, Regińska, Wakulicz)
Discrete ill-posed problems (Regińska)
Inverse problems for partial differential equation and regularization methods (Regińska, Wakulicz, Deriaz)

A seminar organized by the Laboratory covers a wide scope of numerics and attracts attention of mathematicians from other institutes.

The laboratory also organized at the Banach Center mini-schools, directed especially towards young researchers: Regularization methods for ill-posed problems of analysis and statistics – lectures of S. Pereverzyev, (15-25 May 2007); Course on inverse and ill-posed problems – lectures of Andreas Neubauer (26-29 March 2008).

Selected publications:

S. Piszczatowski, K. Skalski, G. Sugocki and A. Wakulicz, Finite element method formulation for the interactions between various elastic-viscoelastic structures in biomechanical model, in: Computer Methods in Biomechanics & Biomedical Engineering-2, J. Middleton, M. L. Jones and G. N. Pande (eds.), Gordon and Breach, (1998), 313-320.
L. Eldén F Berntsson, T. Regińska, Wavelet and Fourier methods for solving the sideways heat equation, SIAM J. Sci. Comput. Vol 21, No.6, pp. 2187-2205, (2000)
T.Regińska, L.E ldén, Stability and convergence of wavelet-Galerkin method for sideways heat equation, J. Inverse and Ill-Posed Problems, vol. 8, no.1, pp. 31-49 (2000)
T. Regińska, Application of wavelet shrinkage to solving sideways heat equation, BIT vol.41, no 5, pp. 1101-1110 (2001)
T.Regińska, Regularization parameters choosing for discrete ill-posed problems, in "Inverse Problems in Engineering Mechanics IV" (Proceedings of the International Symposium on ISIP2003) M.Tanaka (ed.), Elsevier 2003, pp. 457-464.
T. Regińska, Regularization of discrete ill-posed problems, BIT Numerical Mathematics vol.44, pp. 119-133 (2004)
W. Grzesikiewicz, A. Wakulicz, Axiomatic formulation of thermodynamics ideal gas laws, KONES Journal of Powertrian and Transport vol .13. no. 103-110 (2006)
T. Regińska, K. Regiński, Approximate solution of a Cauchy problem for the Helmholtz equation, Inverse Problems 22, pp. 975-989 (2006)
Erwin Deriaz, Valérie Perrier "Direct Numerical Simulation of turbulence using divergence-free wavelets",Preprint IMPAN nr 684, June 2007, SIAM Multiscale Modeling & Simulation, in print
T. Regińska, A. Wakulicz, Wavelet moment method for Cauchy problem for the Helmholtz equation, Journal of Comp. and Appl. Math, (2008), doi:10.1016/j.cam.2008.01.005.
W. Arendt, T. Regińska, An ill-posed boundary value problem for the Helmholtz equation on Lipschitz domain, Ulmer Seminare 2007, Journal of Inverse and Ill-Posed Problems, in print