Alfred Schmidt, IAM Univ. Freiburg Dr. Alfred Schmidt
0761/203-5644

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Current address (since October, 2000):
Zentrum für Technomathematik, Universität Bremen
Tel: (0421) 218-4814 or -2924 (Sekr.), Fax: (0421) 218-4863

My webpage in Bremen: http://www.math.uni-bremen.de/~schmidt

Projects --- Pictures --- Publications --- Private

Simulation of a dendrite growing from a small seed crystal

Projects

I am working on adaptive finite element methods:

Adaptive finite element methods for free boundary problems
BMBF project "Numerische Simulation des vertikalen Bridgman-Verfahrens" (joint with E. Bänsch, K.W. Benz, S. Boschert, G. Dziuk, B. Höhn, T. Kaiser, K.G. Siebert)
BMBF project "Simulation und Optimierung der Flüssigphasenepitaxie bei der Herstellung von Infrarotdetektoren" (joint with K.W. Benz, P. Dold, K.-M. Lin, G. Dziuk, O. Kriessl, K.G. Siebert)
Project "Effiziente Simulation und Numerische Analysis der Dynamik von Dendriten" in the DFG-Schwerpunkt "Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme" (joint with G. Dziuk, M. Fried, A. Veeser)
DFG project "Numerik für 3D Marangonikonvektion bei der Kristallzüchtung in Halbleiterschmelzen mit freier Oberfläche" (joint with E. Bänsch, K.W. Benz, G. Dziuk, B. Höhn, T. Kaiser)
Data structures for adaptive hierarchical FE methods and aspects of efficient implementation
Adaptive h-p FE methods
Adaptive finite element methods in general: Our department's AFEM page

Some pictures from projects or publications

Click on thumbnail for corresponding project or publication

Click here for larger images with short descriptions

Publications

with K.G.Siebert: ALBERT: Software for scientific computations and applications, 15 p., Preprint 41/2000 Freiburg, to appear in Acta Math. Univ. Comenianae
with St. Boschert & K.G. Siebert: Numerical Simulation of Crystal Growth by the Vertical Bridgman Method. in J.S. Szmyd and K. Suzuki (Eds.): Modelling of Transport Phenomena in Crystal Growth, Development in Heat Transfer Series, Vol. 6, WIT Press (2000), 61-96.
with Z.Chen & R.H.Nochetto: A characteristic Galerkin method with adaptive error control for the continuous casting problem. Comp. Meth. Appl. Mech. Engrg. 189 (2000), 249-276.
with K.G.Siebert: A posteriori estimators for the h-p version of the finite element method in 1d. Applied Numerical Mathematics 35 (2000), 43-66.
with Z.Chen & R.H.Nochetto: Error Control and Adaptivity for a Phase Relaxation Model. M2AN 34 (2000), 775-797.
with St. Boschert, K.G.Siebert, E.Bänsch, K.W. Benz, G. Dziuk, Th. Kaiser: Simulation of industrial crystal growth by the vertical Bridgman method. Report 00-11 ZeTeM Bremen und Preprint 14/2000 Freiburg, 16 p.
with K.G.Siebert: ALBERT: An adaptive hierarchical finite element toolbox. Manual, 244 p., Preprint 06/2000 Freiburg.
with E.Bänsch: Simulation of dendritic crystal growth with thermal convection. Interfaces and Free Boundaries 2 (2000), 95-115.
with R.H.Nochetto & C.Verdi: A posteriori error estimation and adaptivity for degenerate parabolic problems. Math. Comput. 69 (2000), 1-24.
with R.H.Nochetto & C.Verdi: Adaptive solution of parabolic free boundary problems with error control. in I. Athanasopoulos, G. Makrakis, and J.F. Rodrigues (Eds.): Free Boundary Problems: Theory and Applications, Chapman & Hall / CRC Research Notes in Mathematics 409 (1999), 344-355.
with K.G.Siebert: Abstract data structures for a finite element package: Design principles of ALBERT. Z. Angew. Math. Mech. 79, Suppl. 1, 49-52 (1999).
with G.Dziuk: Kristalle wachsen im Rechner. To appear in Forschung, DFG (Hrsg.), 3 p.
with K.G.Siebert: Concepts of the finite element toolbox ALBERT. Preprint 17/1998 Freiburg, 12 p., to appear in Notes on Numerical Fluid Mechanics.
with St. Boschert, Th. Kaiser, K.G.Siebert, K.W. Benz, and G. Dziuk: Global simulation of (Cd,Zn)Te single crystal growth by the vertical Bridgman technique. in Modelling and Simulation Based Engineering, S.N. Atluri and P.E. O'Donoghue (Eds.), Tech Science Press, Palmdale (1998).
Approximation of crystalline dendrite growth in two space dimensions. Acta Math. Univ. Comenianae 67 (1998), 57-68.
with R.H.Nochetto & C.Verdi: Adaptive solution of phase change problems over unstructured tetrahedral meshes. In M.Bern, J.E.Flaherty, and M.Luskin (eds.): Grid Generation and Adaptive Algorithms, IMA VMA 113 (1999), 163-181.
with R.H.Nochetto & C.Verdi: Adapting meshes and time-steps for phase change problems. Rend. Mat. Acc. Lincei s. 9, v. 8 (1997), 273-292
with R.H.Nochetto & C.Verdi: Error control for phase change problems. In P. Argoul, F. Fremond, and Q.S. Nguyen (Eds.): IUTAM Symposium on Variations of Domains and Free-Boundary Problems in Solid Mechanics, Solid Mechanics and its Applications Vol. 66, Kluwer (1999), 53-61
with K.G.Siebert: Numerical Aspects of Parabolic Free Boundary Problems - Adaptive Finite Element Methods. Manuscript 70 p., Freiburg/Jyväskylä (1997)
Computation of three dimensional dendrites with finite elements. Journal of Computational Physics 125 (1996), 293-312
with M.Rumpf & K.G.Siebert: Functions defining Arbitrary Meshes - A Flexible Interface between Numerical Data and Visualization Routines. Computer Graphics Forum 15 (1996), 129-141
with M.Rumpf & K.G.Siebert: On a unified visualization approach for data from advanced numerical methods. In R. Scateni, J. Van Wijk, P. Zanarini (eds.): Visualization in Scientific Computing '95, Springer (1995), 35-44
with C. Bandle, A. Brillard, G. Dziuk: Course on Mean Curvature Flow. Manuscript 75 p., Freiburg (1994)
Die Berechnung dreidimensionaler Dendriten mit Finiten Elementen. Preprint no. 332, SFB 256 Bonn (1993)
with E.Bänsch: A Finite Element Method for Dendritic Growth. In: Computational Crystal Growers Workshop, AMS Selected Lectures in Mathematics (1992), 16-20
with M. Rumpf et al.: GRAPE, GRAphics Programming Environment, Report 8, SFB 256, Bonn (1990)
with H. Stenzel: Dreidimensionale graphische Datenverarbeitung. Lecture notes 1988, 1989, 1990, Carl-Cranz-Gesellschaft Oberpfaffenhofen, last one 223 p.
with H. Duvenbeck: Darstellung 2- und 3-dimensionaler Strömungen, in H. Jürgens, D. Saupe (Hrsg.): Visualisierung in Mathematik und Naturwissenschaften, Springer (1989)
with H. Stenzel: Graphik in TeX-Texten und Texte in GKS-Graphiken, Informationstechnik it 28/6, 348-351, Oldenbourg (1986)
with H. Stenzel, G. Herken, B. Schulze: Integration von Computer-unterstütztem Satz und Computer-Graphik, in F. Nake (Hrsg.): Graphik in Dokumenten, Informatik-Fachberichte 19, 113-123, Springer (1986)
Thin Plate Spline-Approximation durch Interpolation mit freien Knoten. Diplomarbeit, 68 p., Bonn (1985)