Wolfgang Hackbusch

16.8k total citations · 4 hit papers
213 papers, 10.0k citations indexed

About

Wolfgang Hackbusch is a scholar working on Computational Mechanics, Computational Theory and Mathematics and Atomic and Molecular Physics, and Optics. According to data from OpenAlex, Wolfgang Hackbusch has authored 213 papers receiving a total of 10.0k indexed citations (citations by other indexed papers that have themselves been cited), including 86 papers in Computational Mechanics, 80 papers in Computational Theory and Mathematics and 59 papers in Atomic and Molecular Physics, and Optics. Recurrent topics in Wolfgang Hackbusch's work include Advanced Numerical Methods in Computational Mathematics (69 papers), Matrix Theory and Algorithms (55 papers) and Electromagnetic Scattering and Analysis (47 papers). Wolfgang Hackbusch is often cited by papers focused on Advanced Numerical Methods in Computational Mathematics (69 papers), Matrix Theory and Algorithms (55 papers) and Electromagnetic Scattering and Analysis (47 papers). Wolfgang Hackbusch collaborates with scholars based in Germany, Switzerland and Spain. Wolfgang Hackbusch's co-authors include Boris N. Khoromskij, Lars Grasedyck, Steffen Börm, Zenon P. Nowak, Stefan Sauter, Simone Kühn, Dietrich Braess, Mario Bebendorf, Mike Espig and I. P. Gavrilyuk and has published in prestigious journals such as The Journal of Chemical Physics, Physical review. B, Condensed matter and Physical Review B.

In The Last Decade

Wolfgang Hackbusch

210 papers receiving 8.8k citations

Hit Papers

Multi-Grid Methods and Applications 1985 2026 1998 2012 1985 1999 1994 2012 400 800 1.2k
What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

  1. Multi-Grid Methods and Applications
    1985 1.5k citations Wolfgang Hackbusch profile →
  2. A Sparse Matrix Arithmetic Based on $\Cal H$ -Matrices. Part I: Introduction to ${\Cal H}$ -Matrices
    1999 769 citations Wolfgang Hackbusch Computing profile →
  3. Iterative Solution of Large Sparse Systems of Equations
    1994 476 citations Wolfgang Hackbusch profile →
  4. Tensor Spaces and Numerical Tensor Calculus
    2012 352 citations Wolfgang Hackbusch profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name h Career Trend Papers Cites
Wolfgang Hackbusch Germany 46 4.1k 3.6k 3.4k 2.4k 2.1k 213 10.0k
James Demmel United States 59 2.8k 0.7× 6.8k 1.9× 2.4k 0.7× 2.9k 1.2× 620 0.3× 289 17.8k
Christian Lubich Germany 43 3.4k 0.8× 2.4k 0.7× 1.9k 0.6× 2.2k 0.9× 980 0.5× 126 11.0k
Vladimir Rokhlin United States 50 2.9k 0.7× 1.9k 0.5× 8.9k 2.6× 6.7k 2.8× 2.8k 1.4× 127 16.2k
H.A. van der Vorst Netherlands 39 4.7k 1.2× 5.7k 1.6× 3.6k 1.0× 1.9k 0.8× 819 0.4× 88 11.8k
Christoph Schwab Switzerland 49 3.9k 1.0× 2.6k 0.7× 635 0.2× 898 0.4× 1.6k 0.8× 307 8.2k
Lloyd N. Trefethen United Kingdom 54 5.4k 1.3× 3.9k 1.1× 2.5k 0.7× 2.1k 0.9× 1.4k 0.7× 175 17.4k
Iain Duff United Kingdom 42 2.5k 0.6× 5.1k 1.4× 1.8k 0.5× 2.0k 0.8× 557 0.3× 141 10.1k
Michele Benzi United States 39 3.4k 0.8× 5.3k 1.4× 3.5k 1.0× 611 0.3× 428 0.2× 113 7.3k
Martin H. Schultz United States 26 5.0k 1.2× 4.1k 1.1× 2.7k 0.8× 2.4k 1.0× 1.3k 0.6× 88 11.7k
J. H. Wilkinson United Kingdom 37 1.7k 0.4× 5.9k 1.6× 2.2k 0.6× 1.7k 0.7× 779 0.4× 96 13.0k

Countries citing papers authored by Wolfgang Hackbusch

Since Specialization
Citations

This map shows the geographic impact of Wolfgang Hackbusch's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Wolfgang Hackbusch with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Wolfgang Hackbusch more than expected).

Fields of papers citing papers by Wolfgang Hackbusch

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Wolfgang Hackbusch. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Wolfgang Hackbusch. The network helps show where Wolfgang Hackbusch may publish in the future.

Co-authorship network of co-authors of Wolfgang Hackbusch

This figure shows the co-authorship network connecting the top 25 collaborators of Wolfgang Hackbusch. A scholar is included among the top collaborators of Wolfgang Hackbusch based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Wolfgang Hackbusch. Wolfgang Hackbusch is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Falcó, Antonio, Wolfgang Hackbusch, & Anthony Nouy. (2023). Geometry of tree-based tensor formats in tensor Banach spaces. Annali di Matematica Pura ed Applicata (1923 -). 202(5). 2127–2144.
2.
Hackbusch, Wolfgang & André Uschmajew. (2016). On the interconnection between the higher-order singular values of real tensors. Numerische Mathematik. 135(3). 875–894. 9 indexed citations
3.
Litvinenko, Alexander, et al.. (2012). Approximation of the stochastic Galerkin matrix in the low‐rank canonical tensor format. PAMM. 12(1). 785–788. 1 indexed citations
4.
Borchardt, M., R. Kleiber, & Wolfgang Hackbusch. (2012). A fast solver for the gyrokinetic field equation with adiabatic electrons. Journal of Computational Physics. 231(18). 6207–6212. 3 indexed citations
5.
Hackbusch, Wolfgang, et al.. (2011). Multigrid solver for the reference interaction site model of molecular liquids theory. Journal of Computational Chemistry. 32(9). 1982–1992. 16 indexed citations
6.
Hackbusch, Wolfgang & Boris N. Khoromskij. (2007). Tensor-product approximation to operators and functions in high dimensions. Journal of Complexity. 23(4-6). 697–714. 57 indexed citations
7.
Hackbusch, Wolfgang, et al.. (2006). Coarsening of Boundary-element Spaces. Computing. 77(3). 253–273. 1 indexed citations
8.
Hackbusch, Wolfgang, Lars Grasedyck, & Steffen Börm. (2002). An introduction to hierarchical matrices. Mathematica Bohemica. 127(2). 229–241. 52 indexed citations
9.
Hackbusch, Wolfgang & Boris N. Khoromskij. (2000). A sparse H-matrix arithmetic: general complexity estimates. Journal of Computational and Applied Mathematics. 125(1-2). 479–501. 55 indexed citations
10.
Hackbusch, Wolfgang & Gabriel Wittum. (1998). Multigrid methods V : proceedings of the Fifth European Multigrid Conference, held in Stuttgart, Germany, October 1 - 4, 1996. Springer eBooks. 2 indexed citations
11.
Hackbusch, Wolfgang & Stefan Sauter. (1993). On the efficient use of the Galerkin-method to solve Fredholm integral equations. Applications of Mathematics. 38(4). 301–322. 41 indexed citations
12.
Hackbusch, Wolfgang, et al.. (1991). Parallel algorithms for partial differential equations - Proceedings of the sixth GAMM-seminar - Kiel, January 19-21, 1990. Infoscience (Ecole Polytechnique Fédérale de Lausanne). 13 indexed citations
13.
14.
Hackbusch, Wolfgang. (1989). Integralgleichungen : Theorie und Numerik. 30 indexed citations
15.
Ballmann, Josef, Richard A. Eppler, & Wolfgang Hackbusch. (1988). Panel methods in fluid mechanics with emphasis on aerodynamics : proceedings of the third GAMM-seminar, Kiel, January 16 to 18, 1987. 1 indexed citations
16.
Braess, Dietrich, Wolfgang Hackbusch, & Ulrich Trottenberg. (1985). Advances in multi-grid methods : proceedings of the conference held in Oberwolfach, December 8 to 13, 1984. 2 indexed citations
17.
18.
Hackbusch, Wolfgang. (1984). Multigrid convergence for a singular perturbation problem. Linear Algebra and its Applications. 58. 125–145. 13 indexed citations
19.
Hackbusch, Wolfgang. (1981). Error analysis of the nonlinear multigrid method of the second kind. Applications of Mathematics. 26(1). 18–29. 5 indexed citations
20.
Hackbusch, Wolfgang. (1981). Optimal $H^{p,{p/2}} $ Error Estimates for a Parabolic Galerkin Method. SIAM Journal on Numerical Analysis. 18(4). 681–692. 10 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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