de | en

Articles in Journals

Jens M. Melenk
On condition numbers in hp-FEM with Gauss-Lobatto based shape functions
J. Comput. Appl. Math. ((in press))
Jens M. Melenk and B. Wohlmuth
On residual-based a posteriori error estimation in hp-FEM
Advances in Comput. Math. ((in press))
Wolfgang Busch, Rüdiger Esser and Wolfgang Hackbusch
Extrapolation applied to the method of characteristics for a first order system of two partial differential equations
Numer. Math. 24 (1975), pages 331-353
Wolfgang Hackbusch
Extrapolation applied to certain discretization methods solving the initial value problem for hyperbolic differential equations
Numer. Math. 28 (1977), pages 121-142
Wolfgang Hackbusch
Extrapolation to the limit for numerical solutions of hyperbolic differential equations
Numer. Math. 28 (1977), pages 455-474
Wolfgang Hackbusch
On a method of characteristics for solving a hyperbolic equation of second order
Computing 20 (1978), pages 47-60
Wolfgang Hackbusch
A numerical method for solving parabolic equations with opposite orientations
Computing 20 (1978), pages 229-240
Wolfgang Hackbusch
On the multi-grid method applied to difference equations
Computing 20 (1978), pages 291-306
Wolfgang Hackbusch
On the fast solution of nonlinear elliptic equations
Numer. Math. 32 (1979), pages 83-95
Wolfgang Hackbusch
On the computation of approximate eigenvalues and eigenfunctions of elliptic operators by means of a multi-grid method
SIAM J. Numer. Anal. 16 (1979), pages 201-215
Wolfgang Hackbusch
On the fast solving of parabolic boundary control problems
SIAM J. Control. Optim. 17 (1979), pages 231-244
Susanne Dittrich and Wolfgang Hackbusch
A method of characteristics solving the initial-boundary value problem of a hyperbolic differential equation of second order
Numer. Math. 34 (1980), pages 217-234
Wolfgang Hackbusch
Convergence of multi-grid iterations applied to difference equations
Math. Comp. 34 (1980), pages 425-440
Wolfgang Hackbusch
The fast numerical solution of very large elliptic difference schemes
J. Inst. Maths. Applics. 26 (1980), pages 119-132
Wolfgang Hackbusch and Götz Hofmann
Results of the eigenvalue problem for the plate equation
Z. Angew. Math. Phys. 31 (1980), pages 730-739
Wolfgang Hackbusch
Fast solution of elliptic control problems
J. Optim. Theory Appl. 31 (1980), pages 565-581
Wolfgang Hackbusch
Die schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art
Beiträge Numer. Math. 9 (1981), pages 47-62
Files:
Postscript (reconstructed) , PDF (reconstructed)
Wolfgang Hackbusch
On the convergence of multi-grid iterations
Beiträge Numer. Math. 9 (1981), pages 213-239
Wolfgang Hackbusch
Error analysis of the nonlinear multi-grid method of the second kind
Aplikace Matematiky 26 (1981), pages 18-29
Wolfgang Hackbusch
On the regularity of difference schemes
Ark. Mat. 19 (1981), pages 71-95
Wolfgang Hackbusch
Optimal Hp,p/2 error estimates for a parabolic Galerkin method
SIAM J. Numer. Anal. 18 (1981), pages 681-692
Wolfgang Hackbusch
Fast numerical solution of time-periodic parabolic problems by a multi-grid method
SIAM J. Sci. Statist. Comput. 2 (1981), pages 198-206
Wolfgang Hackbusch
Bemerkungen zur iterativen Defektkorrektur und zu ihrer Kombination mit Mehrgitterverfahren
Rev. Roumaine Math. Pures Appl. 26 (1981), pages 1319-1329
Files:
Postscript (reconstructed) , PDF (reconstructed)
Wolfgang Hackbusch
A note on the penalty correction method
Zeitschrift für Analysis und ihre Anwendungen 2 (1982), pages 59-69
Wolfgang Hackbusch
On the regularity of difference schemes Part II: regularity estimates for linear and nonlinear problems
Ark. Mat. 21 (1983), pages 3-28
Wolfgang Hackbusch and Hans D. Mittelmann
On multi-grid methods for variational inequalities
Numer. Math. 42 (1983), pages 65-76
Dittrich Braess and Wolfgang Hackbusch
A new convergence proof for the multigrid method including the V-cycle
SIAM J. Numer. Anal. 20 (1983), pages 967-975
Wolfgang Hackbusch and Thomas Will
A numerical method for a parabolic bang-bang problem
Control Cybernet. 12 (1983), pages 99-116
Wolfgang Hackbusch
Multi-grid solutions to linear and nonlinear eigenvalue problems for integral and differential equations
Rostock Math. Colloq. 25 (1984), pages 79-98
Wolfgang Hackbusch
Local defect correction method and domain decomposition techniques
Computing, Suppl. 5 (1984), pages 89-113
Wolfgang Hackbusch
Multi-grid convergence for a singular perturbation problem
Linear Algebra Appl. 58 (1984), pages 125-145
Wolfgang Hackbusch
Schnelle Löser für partielle Differentialgleichungen
PM Mathematik 27 (1985), pages 478-501
Wolfgang Hackbusch and Zenon Paul Nowak
On the fast matrix multiplication in the boundary element method by panel clustering
Numer. Math. 54 (1989), pages 463-491
Wolfgang Hackbusch
On first and second order box schemes
Computing 41 (1989), pages 277-296
Wolfgang Hackbusch and Arnold Reusken
Analysis of a damped nonlinear multilevel method
Numer. Math. 55 (1989), pages 225-246
Wolfgang Hackbusch
The frequency decomposition multi-grid method. Part I: Application to anisotropic equations
Numer. Math. 56 (1989), pages 229-245
Wolfgang Hackbusch
The solution of large systems of BEM equations by the multi-grid and panel clustering technique
Rend. Sem. Mat. Univers. Politecn. Torino Fasciolo Speciale (1991), pages 163-187
Wolfgang Hackbusch
Iterationsverfahren für große Gleichungssysteme
Jber. d. Dt. Math.-Verein. Sonderband Jubiläumstagung 1990 (1992), pages 124-137
Wolfgang Hackbusch
Comparison of different multi-grid variants for nonlinear equations
ZAMM 72 (1992), pages 148-151
Wolfgang Hackbusch
The frequency decomposition multi-grid method. Part II: Convergence analysis based on the additive Schwarz method
Numer. Math. 63 (1992), pages 433-453
Wolfgang Hackbusch
A parallel conjugate gradient method
Numerical Linear Algebra with Applications 1 (1992), pages 133-147
Wolfgang Hackbusch and Stefan A. Sauter
On the efficient use of the Galerkin method to solve Fredholm integral equations
Applications of Mathematics 38 (1993), pages 301-322
Wolfgang Hackbusch and Stefan A. Sauter
On numerical cubatures of nearly singular surface integrals arising in BEM collocation
Computing 52 (1994), pages 139-159
Wolfgang Hackbusch
A note on Reusken's lemma
Computing 55 (1995), pages 181-189
Wolfgang Hackbusch and Stefan A. Sauter
Adaptive composite finite elements for the solution of PDEs containing non-uniformly distributed micro-scales
Matematicheskoe modelirovanie 8 (1996), pages 31-43
I. Babuska, B. Andersson, B. Guo, J.M. Melenk and H.S. Oh
Finite Element Method for Problems with Singular Solutions
Comput. Appl. Math. 74 (1996), pages 51-70
J.M. Melenk and I. Babuska
The partition of unity finite element method: Basic theory and applications
Comput. Meths. Appl. Mech. Eng. 139 (1996), pages 289-314
J.M. Melenk and G. Zimmermann
Functions with time and frequency gaps
J.~Fourier Anal. Appl. 2 (1996), pages 611-614
Wolfgang Hackbusch
Numerische Mathematik und ihre Wechselwirkung mit der gegenwärtigen Rechnerentwicklung
Berlin-Brandenburgische Akademie der Wissenschaften 4 (1997), pages 55-67
Wolfgang Hackbusch and Stefan A. Sauter
Composite finite elements for the approximation of PDEs on domains with complicated micro-structures
Numer. Math. 75 (1997), pages 447-472
Wolfgang Hackbusch and Stefan A. Sauter
Composite finite elements for problems containing small geometric details, Part II: Implementation and numerical results
Comput. Visual. Sci. 1 (1997), pages 15-25
Wolfgang Hackbusch
On the feedback vertex set problem for a planar graph
Computing 58 (1997), pages 129-155
Wolfgang Hackbusch and Thomas Probst
Downwind Gauß-Seidel smoothing for convection dominated problems
Numerical Linear Algebra with Applications 4 (1997), pages 85-102
Maksimilian Dryja and Wolfgang Hackbusch
On the nonlinear domain decomposition method
BIT 37 (1997), pages 296-311
S. Lorenz, C. Solterbeck, Wolfgang Schattke, Jens Burmeister and Wolfgang Hackbusch
Electron scattering states at solid surfaces calculated with realistic potentials
Rapid Communications bei Phys. Rev. B 55 (1997), pages R13 432-435
I. Babuska and J.M. Melenk
The partition of unity method
Int. J. Numer. Meths. Eng. 40 (1997), pages 727-758
J. M. Melenk
On the robust exponential convergence of hp finite element methods for problems with boundary layers
IMA J. Numer. Anal. 17 (1997), pages 577-601
J. M. Melenk and I. Babuska
Approximation with Harmonic and Generalized Harmonic Polynomials in the Partition of Unity Method
Comput. Assist. Mech. Eng. Sciences 4 (1997), pages 607-632
Peter Bastian, Wolfgang Hackbusch and Gabriel Wittum
Additive and multiplicative multi-grid - a comparison
Computing 60 (1998), pages 345-364
Wolfgang Hackbusch and Jens Uwe Wappler
Remarks on a posteriori error estimation for inaccurate finite element solutions
Computing 60 (1998), pages 175-191
Wolfgang Hackbusch and Stefan A. Sauter
A new finite element approach for problems containing small geometric details
Archivum mathematicum 34 (1998), pages 105-117
Files:
Postscript (reconstructed) , PDF (reconstructed)
Wolfgang Hackbusch
From classical numerical mathematics to scientific computing
Doc. Math. J. DMV Extra Volume ICM I (1998), pages 95-114
J. M. Melenk and C. Schwab
hp FEM for Reaction-Diffusion Equations I: Robust Exponentional Convergence
SIAM J. Numer. Anal. 35 (1998), pages 1520-1557
Dietrich Braess, Maksimilian Dryja and Wolfgang Hackbusch
Grid transfer for nonconforming FE-discretisations with application to non-matching grids
Computing 63 (1999), pages 1-25
Wolfgang Hackbusch
A sparse matrix arithmetic based on H-matrices. Part I: Introduction to H-matrices
Computing 62 (1999), pages 89-108
Files:
Postscript , PDF
J. M. Melenk
Operator adapted spectral element methods. I: Harmonic and Generalized Harmonic Polynomials
Numer. Math. 84 (1999), pages 35-69
J. M. Melenk and C. Schwab
Analytic Regularity for a Singularly Perturbed Problem
SIAM J. Math. Anal. 30 (1999), pages 379-400
J. M. Melenk and C. Schwab
An hp FEM for convection-diffusion problems in one dimension
IMA J. Numer. Anal. 19 (1999), pages 425-453
J. M. Melenk and C. Schwab
The hp-streamline diffusion method for convection dominated problems in one space dimension
East-West J. Numer. Anal. 7 (1999), pages 31-60
Wolfgang Hackbusch and Boris N. Khoromskij
A sparse H-matrix arithmetic. Part II: Application to multi-dimensional problems
Computing 64 (2000), pages 21-47
Further Version:
[Preprint]
Wolfgang Hackbusch and Boris N. Khoromskij
A sparse H-matrix arithmetic: general complexity estimates
Journal of Computational and Applied Mathematics 125 (2000), pages 479-501
Further Version:
[Preprint]
Mario Bebendorf
Approximation of boundary element matrices
Numerische Mathematik 86 (2000), pages 565-589
Further Version:
[Preprint]
Ivan G. Graham, Wolfgang Hackbusch and Stefan A. Sauter
Discrete boundary element methods on general meshes in 3D
Numer. Math. 86 (2000), pages 103-137
Ivan G. Graham, Wolfgang Hackbusch and Stefan A. Sauter
The hybrid Galerkin boundary element method: theory and implementation
Numer. Math. 86 (2000), pages 139-172
J. M. Melenk
On n-widths for elliptic problems
J. Math. Anal. Appl. 274 (2000), pages 272-289
J. M. Melenk, N. P. Kirchner and C. Schwab
Spectral Galerkin discretizations for hydrodynamic stability problems
Computing 65 (2000), pages 97-118
Steffen Börm and Ralf Hiptmair
Analysis of Tensor Product Multigrid
Numerical Algorithms 26 (2001), pages 219-234
Further Version:
[Preprint]
Steffen Börm
Tensor Product Multigrid for Maxwell's Equation with Aligned Anisotropy
Computing 66 (2001), pages 321-342
Further Version:
[Preprint]
Wolfgang Hackbusch
The efficient computation of certain determinants arising in the treatment of Schrödinger's equations
Computing 67 (2001), pages 35-56
Further Version:
[Preprint]
Iwan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij
H-matrix approximation for elliptic solutions operators in cylindric domains
East-West J. Numer. Math. 9 (2001), pages 25-58
Further Version:
[Preprint]
J. M. Melenk, K. Gerdes and C. Schwab
Fully discrete hp-FEM: fast quadrature
Comput. Meth. Appl. Mech. Eng. 190 (2001), pages 4339-4364
K. Gerdes, J. M. Melenk, D. Schötzau and C. Schwab
The hp-version of the Streamline-Diffusion Finite Element Method in two space dimensions
M3AS 11 (2001), pages 301-337
J. M. Melenk and T. Gutzmer
Approximation orders for natural splines in arbitrary dimensions
Math. Comput. 70 (2001), pages 699-703
Steffen Börm and Ralf Hiptmair
Multigrid Computation of Axisymmetric Electromagnetic Fields
Advances in Computational Mathematics 16 (2002), pages 331-356
Further Version:
[Preprint]
Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij
H-matrix approximation for the operator exponential with applications
Numerische Mathematik 92 (2002), pages 83-111
Further Version:
[Preprint]
Wolfgang Hackbusch and Boris N. Khoromskij
Blended kernel approximation in the H-matrix techniques
Numerical Linear Algebra with Applications 9 (2002), pages 281-304
Further Version:
[Preprint]
Wolfgang Hackbusch
Direct integration of the Newton potential over cubes including a program description
Computing 68 (2002), pages 193-216
Further Version:
[Preprint]
Steffen Börm and Wolfgang Hackbusch
Data-sparse approximation by adaptive H2-matrices
Computing 69 (2002), pages 1-35
File:
PDF
Further Version: [Preprint]
Heinz-Jürgen Flad, Wolfgang Hackbusch, Dietmar Kolb and Reinhold Schneider
Wavelet approximation of correlated wavefunctions. I. Basics
Journal of Chemical Physics 116 (2002), pages 9641-9657
Further Version:
[Preprint]
Heinz-Jürgen Flad, Wolfgang Hackbusch, Dietmar Kolb and Hongjun Luo
Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes
Journal of Chemical Physics 117 (2002), pages 3625-3638
Further Version:
[Preprint]
Steffen Börm and Wolfgang Hackbusch
H2-matrix approximation of integral operators by interpolation
Appl. Numer. Math. 43 (2002), pages 129-143
Further Version:
[Preprint]
B. N. Khoromskij and Jens M. Melenk
An efficient direct solver for the Boundary concentrated FEM in 2D
Computing 69 (2002), pages 91-117
Further Version:
[Preprint]
Mario Bebendorf and Sergej Rjasanow
Adaptive Low-Rank Approximation of Collocation Matrices
Computing 70 (2003), pages 1-24
Further Version:
[Preprint]
B. N. Khoromskij and Jens M. Melenk
Boundary concentrated finite element methods
SIAM Journal on Numerical Analysis 41 (2003), pages 1-36
Further Version:
[Preprint]
Steffen Börm, Lars Grasedyck and Wolfgang Hackbusch
Introduction to hierarchical matrices with applications
Engineering Analysis with Boundary Elements 27 (2003), pages 405-422
Further Version:
[Preprint]
Mario Bebendorf and Wolfgang Hackbusch
Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with Loo-Coefficients
Numerische Mathematik 95 (2003), pages 1-28
Further Version:
[Preprint]
Lars Grasedyck, Wolfgang Hackbusch and Boris N. Khoromskij
Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices
Computing 70 (2003), pages 121-165
Further Version:
[Preprint]
Lars Grasedyck and Wolfgang Hackbusch
Construction and Arithmetics of H-Matrices
Computing 70 (2003), pages 295-334
Further Version:
[Preprint]
Wolfgang Dahmen, Birgit Faermann, Ivan G. Graham, Wolfgang Hackbusch and Stefan A. Sauter
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method
Math. Comp. 73 (2004), pages 1107-1138
File:
Online
Further Version: [Preprint]
Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij
Data-sparse approximation to the operator-valued functions of elliptic operators
Math. Comp. 73 (2004), pages 1297-1324
Further Version:
[Preprint]
Steffen Börm
H2-matrices - Multilevel methods for the approximation of integral operators
Computing and Visualization in the Sciences 7 (2004), pages 173-181
Further Version:
[Preprint]
Lars Grasedyck, Wolfgang Hackbusch and Sabine LeBorne
Adaptive geometrically balanced clustering of H-matrices
Computing 73 (2004), pages 1-23
Further Version:
[Preprint]
Lars Grasedyck, Wolfgang Hackbusch and Carsten Wolters
Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem
Inverse Problems 20 (2004), pages 1099-1116
Wolfgang Hackbusch, Boris N. Khoromskij and Ronald Kriemann
Hierarchical matrices based on a weak admissibility criterion
Computing 73 (2004), pages 207-243
Steffen Börm, Maike Löhndorf and Jens M. Melenk
Approximation of integral operators by variable-order interpolation
Numerische Mathematik 99 (2005), pages 605-643
Further Version:
[Preprint]
Ivan G. Graham, Wolfgang Hackbusch and Stefan A. Sauter
Finite elements on degenerate meshes: Inverse-type inequalities and applications
IMA Journal of Numerical Analysis 25 (2005), pages 379-407
Further Version:
[Preprint]
Wolfgang Hackbusch, Boris N. Khoromskij and Eugene E. Tyrtyshnikov
Hierarchical Kronecker tensor-product approximations
Journal of Numerical Mathematics 13 (2005), pages 119-156
Further Version:
[Preprint]
Ivan P. Gavrilyuk, Wolfgang Hackbusch and Boris N. Khoromskij
Data-sparse approximation of a class of operator-valued functions
Math. Comp. 74 (2005), pages 681-708
Further Version:
[Preprint]
Steffen Börm and Wolfgang Hackbusch
Hierarchical Quadrature of Singular Integrals
Computing 74 (2005), pages 75-100
Further Version:
[Preprint]
Steffen Börm, Nico Krzebek and Stefan A. Sauter
May the singular integrals in BEM be replaced by Zero?
Comp. Meth. Appl. Mech. Eng. 194 (2005), pages 383-393
Further Version:
[Preprint]
Steffen Börm
Approximation of integral operators by H2-matrices
Computing 74 (2005), pages 249-271
Further Version:
[Preprint]
Wolfgang Hackbusch, Boris N. Khoromskij and Ronald Kriemann
Direct Schur complement method by domain decomposition based on H-matrix approximation
Computing and Visualization in the Sciences (2005), pages 179-188
Further Version:
[Preprint]
Heinz-Jürgen Flad, Wolfgang Hackbusch, Hongjun Luo and Dietmar Kolb
Wavelet approach to quasi two-dimensional extended many-particle systems. I. Supercell Hartree-Fock method
Journal of Computational Physics 205 (2005), pages 540-566
Wolfgang Hackbusch and Boris N. Khoromskij
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part I. Separable Approximation of Multi-variate Functions
Computing 76 (2006), pages 177-202
Wolfgang Hackbusch and Boris N. Khoromskij
Low-rank Kronecker-product Approximation to Multi-dimensional Nonlocal Operators. Part II. HKT Representation of Certain Operators
Computing 76 (2006), pages 203-225
Wolfgang Hackbusch
Approximation of 1/|x-y| by Exponentials for Wavelet Applications
Computing 76 (2006), pages 359-366
Further Version:
[Preprint]
Wolfgang Hackbusch, Boris N. Khoromskij and Stefan A. Sauter
Adaptive Galerkin boundary element methods with panel clustering
Numerische Mathematik 105 (2007), pages 603-631