Research Hans Z. Munthe-Kaas


Page last updated by HZMK: May, 2012

Papers (reverse chronology)

Articles: (most of them)

  1. Gunnar Fløystad, Hans Munthe-Kaas: Pre- and post-Lie algebras: The algebro-geometric view, Abel Symposium Series, Springer 2017.

  2. Kurusch Ebrahimi-Fard, Igor Mencattini, Hans Munthe-Kaas: Post-Lie algebras and factorization theorems, J. of Geometry and Physics, 119:19-33, 2017.

  3. Hans Munthe-Kaas: Groups and symmetries in numerical linear algebra. In `Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications, Springer Lecture Notes in Mathematics 2173, 2016.

  4. Kurusch Ebrahimi-Fard, Alexander Lundervold, Igor Mencattini, Hans Munthe-Kaas: Post-Lie algebras and isospectral flows, SIGMA - Symmetry, Integrability, and Geometry: Methods and Applications, 11, 2015.

  5. Hans Munthe-Kaas, Kristoffer Føllesdal: Lie-Butcher series, geometry, algebra and computation. Springer Lectues in Mathematics and Statistics, 2017.

  6. Kurusch Ebrahimi-Fard, Alexander Lundervold, Hans Munthe-Kaas: On the Lie enveloping algebra of a post-Lie algebra. Journal of Lie Theory, 25(4):1139-1165 (2015).

  7. Hans Munthe-Kaas, Olivier Verdier: Integrators on homogeneous spaces: Isotropy choice and connections. J. Found. Comput. Math., 16(4):899-939, 2016.

  8. Robert I. McLachlan, Klas Modin, Hans Munthe-Kaas, Olivier Verdier: B-series methods are exactly the affine equivariant methods. Numerische Mathematik, 133(3):599-622.

  9. Helge Holden, Hans Munthe-Kaas, Dierk Schleicher: Laureates Meet Young Researchers In Heidelberg, EMS Newsletter March 2014.

  10. Hans Munthe-Kaas, Olivier Verdier: Aromatic Butcher series. Found. Comp. Math. 16:183-212, 2016.

  11. Ferenc A. Bartha, Hans Z. Munthe-Kaas: Computing of B-series by automatic differentiation. Discrete and Continuous Dynamical Systems - Ser. A, (2014) 34:903 - 914.

  12. H.Z. Munthe-Kaas, G.R.W. Quispel, A. Zanna: Symmetric spaces and Lie triple systems in numerical analysis of differential equations, BIT Numerical Mathematics (2014) 54:257–282.

  13. H. Z. Munthe-Kaas, M. Nome, B. N. Ryland: Through the Kaleidoscope; Symmetries, Groups and Chebyshev Approximations from a Computational Point of View, Foundations of Computational Mathematics, Budapest 2011 403, 188. London Mathematical Society Lecture Note Series.

  14. H. Z. Munthe-Kaas, A. Lundervold: On post-Lie algebras, Lie–Butcher series and moving frames, Foundations of Computational Mathematics 2013 (4), 583-613.

  15. A. Lundervold, H.Z. Munthe-Kaas: On algebraic structures of numerical integration on vector spaces and manifolds, In Faá di Bruno Hopf algebras, Dyson-Schwinger Equations and Lie-Butcher series, p. 219-264 Eur. Math. Soc..

  16. A. Lundervold, H.Z. Munthe-Kaas: Backward error analysis and the substitution law for Lie group integrators, Foundations of Computational Mathematics 2013 (2), 161-186.

  17. H. Z. Munthe-Kaas, T. Sørevik: Multidimensional pseudo-spectral methods on lattice grids, Applied Numerical Mathematics,Volume 62, Issue 3, March 2012, Pages 155–165.

  18. Kurusch Ebrahimi-Fard, Alexander Lundervold, Simon J. A. Malham, Hans Munthe-Kaas, Anke Wiese, Algebraic structure of stochastic expansions and universally accurate simulation, Proc. Royal Soc. A, 2012.

  19. S. Christiansen, H. Z. Munthe-Kaas, B. Owren: Topics in structure preservation. Acta Numerica 2011.

  20. B.N. Ryland, H.Z. Munthe-Kaas: On multivariate Chebyshev polynomials and spectral approximation on triangles, Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in computational science and engineering, Springer 2011.

  21. A. Lundervold,H.Z. Munthe-Kaas: Hopf algebras of formal diffeomorphisms and numerical integration on manifolds. In ‘Combinatorics and Physics’, Contemporary Mathematics, vol 539, AMS 2011.

  22. S. Krogstad, H.Z. Munthe-Kaas, A. Zanna:  Generalized Polar Coordinates on Lie Groups and Numerical Integrators, Numerische Mathematik (2009) 114:161–187.

  23. H.Z. Munthe-Kaas, B. Owren (eds.) The Abel Symposium 2006, ”Mathematics and Computation, a contemporary view”, Springer (2008).

  24. R.I. McLachlan, H.Z. Munthe-Kaas, G.R.W. Quispel, A. Zanna: Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields, Found. Comput. Math., 8 (2008), no. 3, 335–355.

  25. H. Z. Munthe-Kaas, W. Wright: On the Hopf Algebraic Structure of Lie Group Integrators, Found. Comput.Math.(2007).

  26. H. Z. Munthe-Kaas: On group Fourier analysis and symmetry preserving discretizations of PDEs, J. Phys. A: Math. Gen. 39 (2006) 5563–5584.

  27. M. Haveraaen, H. A. Friis, H Munthe-Kaas: Computable scalar fields: A basis for PDE software, The Journal of Logic and Algebraic Programming 65 (2005) 36-49.

  28. Jialin Hong, Ying Liu, Hans Munthe-Kaas, Antonella Zanna: Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients, Applied Numerical Mathematics 56 (2006) 814–843.

  29. K. Åhlander, H. Munthe-Kaas: Eigenvalues for equivariant matrices, Journal of Computational and Applied Mathematics 192 (2006) 89 – 99.

  30. K. Åhlander, H. Munthe-Kaas: Applications of the Generalized Fourier Transform in Numerical Linear Algebra, BIT Numerical Mathematics (2005) 45: 819–850.

  31. H. Munthe-Kaas, S. Krogstad: On enumeration problems in Lie–Butcher theory, Future Generation Computer Systems 19 (2003) 1197–1205.

  32. K. Åhlander, M. Haveraaen, H. Munthe-Kaas: On Object-Oriented Frameworks and Coordinate Free Formulations of PDEs, Engineering with Computers (2002) 18: 286–294.

  33. J-B Chen, H Munthe-Kaas, M-Z Qin: Square-Conservative Schemes for a Class of Evolution Equations Using Lie-Group Methods, SIAM J. Numer. Anal. Vol. 39, No. 6, pp. 2164–2178 (2002).

  34. H.A. Friis, T. A. Johansen, M. Haveraaen, H. Munthe-Kaas, Å. Drottning: Use of coordinate-free numerics in elastic wave simulation, Applied Numerical Mathematics 39 (2001) 151–171.

  35. K Åhlander , M Haveraaen , H Munthe-Kaas: On the Role of Mathematical Abstractions for Scientific Computing, The architecture of scientific software (Boisvert and Tang eds.), Kluwer acad. publ. (2001), pp. 145-159.

  36. H. Z. Munthe-Kaas, G. R. W. Quispel, A. Zanna: Generalized Polar Decompositions on Lie Groups with Involutive Automorphisms, Found. Comput. Math. (2001) 1:297–324.

  37. A. Zanna, H. Z. Munthe-Kaas: Generalized polar decompositions for approximation of the matrix exponential, SIAM J. Matrix Anal. Appl. Vol. 23, No. 3, pp. 840–862 (2002).

  38. A. Zanna, K. Engø, H. Z. Munthe-Kaas: Adjoint and selfadjoint Lie group methods, BIT 2001, Vol. 41, No. 2, pp. 395–421.

  39. A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, A. Zanna: Lie-group methods, Acta Numerica (2000), pp. 215–365, CUP.

  40. K. Engø, A. Marthinsen, H. Z. Munthe-Kaas: DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds, Applied Numerical Mathematics 39 (2001) 323–347.

  41. S. Faltinsen, A. Marthinsen, H. Z. Munthe-Kaas: Multistep methods integrating ordinary differential equations on manifolds, Applied Numerical Mathematics 39 (2001) 349–365.

  42. H. Z. Munthe-Kaas, B. Owren: Computations in a Free Lie-algebra, Phil. Trans. R. Soc. Lond. A (1999) 357, 957–981.

  43. H. Munthe-Kaas: High order Runge-Kutta methods on manifolds, Applied Numerical Mathematics29 (1999) 115-127.

  44. Hans Munthe-Kaas: Runge-Kutta Methods on Lie groups, BIT 38:1 (1998), 92-111.

  45. A. Zanna, H. Munthe-Kaas: Iterated Commutators, Lie's Reduction Method and Ordinary Differential Equations on Matrix Lie Groups, Foundations of Computational Mathematics, Springer Verlag 1997.

  46. H. Z. Munthe-Kaas, A. Zanna: Numerical integration of differential equations on homogeneous manifolds, Foundations of Computational Mathematics, Springer Verlag 1997.

  47. A. Marthinsen, H. Munthe-Kaas, B. Owren: Simulation of ordinary differential equations on manifolds: some numerical experiments and verifications, Modeling, Identification and Control, 18, 1, pp. 75-88 (1997).

  48. M. Arioli, H. Munthe-Kaas, L. Valdettaro: Componentwise error analysis for FFTs with applications to fast Helmholtz solvers, Numerical algorithms 12(1996)65-88.

  49. H. Munthe-Kaas, M. Haveraaen: Coordinate free numerics : Closing the gap between 'pure' and 'applied' mathematics?, Zeitschrift für angewandte Mathematik und Mechanik, 1996, vol. 76, pp. 487-488.

  50. H. Munthe-Kaas: Lie-Butcher Therory for Runge-Kutta Methods, BIT 35 (1995), 572-587.

  51. H. Munthe-Kaas: Routing K-Tile permutations on Parallel Computers, NIK 1994.

  52. H. Munthe-Kaas, A.M. Skånøy: Modeling Waves in Discontinuous media; Uniformly Converging Schemes, EAEG 55, 1993.

  53. M. Haveraaen, H. Munthe-Kaas, V. Madsen: Algebraic Programming Technology for Partial Differential Equations, NIK 1992.

  54. H. Munthe-Kaas: Generalized Shuffle-Exchange Networks; a brief summary, Springer Lect. Notes in Computer Science 634, 1992.

  55. H. Munthe-Kaas: Superparallel FFTs, SIAM J. Sci Comput., Vol 14, No. 2, pp. 349-367, 1993 J. Scientific and Statistical Comput.

Tech reports, unpublished: (some of them)

  1. H. Munthe-Kaas: An algebraic theory for regular data mappings on parallel computers, Report 102, 1995, Department of Informatics, U. of Bergen, ISSN 0333-3590.

  2. H. Munthe-Kaas: Generalized Shuffle-Exchange networks, Report 61, 1992, Department of Informatics, U. of Bergen, ISSN 0333-3590.

  3. H. Munthe-Kaas: Symmetric FFTs; a general approach, Tech. rep. Department of Math. Sciences, NTNU Trondheim, May 1989.

Thesis: H. Munthe-Kaas: Topics in Linear Algebra for Vector and Parallel Computers, PhD Thesis, NTNU Trondheim, 1989. (Awarded Esso prize for best PhD 1989).