Hjem
Hans Z.  Munthe-Kaass bilde

Hans Z. Munthe-Kaas

Professor, Beregningsmatematikk
  • E-postHans.Munthe-Kaas@uib.no
  • Telefon+47 55 58 41 79+47 452 38 987
  • Besøksadresse
    Realfagbygget, Allégt. 41
    Rom 
    4A7d Realfagbygget
  • Postadresse
    Postboks 7803
    5020 Bergen
Vitenskapelig artikkel
  • 2020. Planarly branched rough paths and rough differential equations on homogeneous spaces. Journal of Differential Equations. 9740-9782.
  • 2020. Invariant connections, Lie algebra actions, and foundations of numerical integration on manifolds. SIAM Journal on applied algebra and geometry. 49-68.
  • 2019. What is a post-Lie algebra and why is it useful in geometric integration. Lecture Notes in Computational Science and Engineering. 429-437.
  • 2019. Pre- and post-lie algebras: The algebro-geometric view. Abel Symposia. 321-367.
  • 2018. Lie-Butcher series, Geometry, Algebra and Computation. Springer Proceedings in Mathematics & Statistics. 71-113.
  • 2017. Post-Lie algebras and factorization theorems. Journal of Geometry and Physics. 19-33.
  • 2016. Integrators on homogeneous spaces: Isotropy choice and connections. Foundations of Computational Mathematics. 183-215.
  • 2016. Groups and symmetries in numerical linear algebra. Lecture notes in mathematics. 319-406.
  • 2015. Post-lie algebras and isospectral flows. SIGMA. Symmetry, Integrability and Geometry.
  • 2015. On the Lie enveloping algebra of a post-Lie algebra. Journal of Lie theory. 1139-1165.
  • 2015. B-series methods are exactly the affine equivariant methods. Numerische Mathematik. 599-622.
  • 2015. Aromatic Butcher Series. Foundations of Computational Mathematics. 185-215.
  • 2014. Symmetric spaces and Lie triple systems in numerical analysis of differential equations. BIT Numerical Mathematics. 257-282.
  • 2014. Computing of B-series by automatic differentiation. Discrete and Continuous Dynamical Systems. Series A. 903-914.
  • 2013. On post-lie algebras, lie-butcher series and moving frames. Foundations of Computational Mathematics. 583-613.
  • 2013. Backward Error Analysis and the Substitution Law for Lie Group Integrators. Foundations of Computational Mathematics. 161-186.
  • 2012. Multidimensional pseudo-spectral methods on lattice grids. Applied Numerical Mathematics. 155-165.
  • 2012. Algebraic structure of stochastic expansions and efficient simulation. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. 2361-2382.
  • 2011. On Multivariate Chebyshev Polynomials and Spectral Approxi- mations on Triangles. Lecture Notes in Computational Science and Engineering. 19-41.
  • 2011. Hopf algebras of formal diffeomorphisms and numerical integration on manifolds. Contemporary Mathematics.
  • 2009. Generalized polar coordinates on Lie groups and numerical integrators. Numerische Mathematik. 161-187.
  • 2008. On the Hopf algebraic structure of Lie group integrators. Foundations of Computational Mathematics. 227-257.
  • 2008. Explicit Volume-Preserving Splitting Methods for Linear and Quadratic Divergence-Free Vector Fields. Foundations of Computational Mathematics. 335-355.
  • 2006. On group Fourier analysis and symmetry preserving discretizations of PDEs. Journal of Physics A: Mathematical and General. 5563-5584.
  • 2006. Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients. Applied Numerical Mathematics. 814-843.
  • 2006. Eigenvalues for equivariant matrices. Journal of Computational and Applied Mathematics. 89-99.
  • 2005. Computable Scalar Fields: a basis for {PDE} software. Journal of Logic and Algebraic Programming. 36-49.
  • 2005. Applications of the generalized Fourier transform in numerical linear algebra. BIT Numerical Mathematics. 819-850.
  • 2002. On Object-Oriented Frameworks and Coordinate Free Formulations of {PDE}s. Engineering with Computers. 286-294.
  • 2001. Use of coordinate free numerics in elastic wave simulation. Applied Numerical Mathematics. 151-171.
  • 2001. Multistep methods integrating ordinary differential equations on manifolds. Applied Numerical Mathematics. 349-365.
  • 2001. Generalized Polar Decompositions on Lie Groups witn Involutive Automorphisms. Found. Comput. Math.. 297-324.
  • 2001. Generalized Polar Decompositions for the Approximation of the Matrix Exponential. SIAM Journal on Matrix Analysis and Applications. 840-862.
  • 2001. DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds. Applied Numerical Mathematics. 323-347.
  • 2001. Adjoint and self-adjoint Lie-group methods. BIT Numerical Mathematics. 395-421.
  • 2000. Lie-group methods. Acta Numerica. 215-365.
  • 1999. High order Runge-Kutta methods on Manifolds. Applied Numerical Mathematics. 115-127.
  • 1999. Computations in a Free Lie Algebra. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 957-981.
  • 1997. Simulation of ordinary differential equations on manifolds : some numerical experiments and verifications. Modeling, Identification and Control. 75-88.
  • 1993. Superparallel FFTs. SIAM Journal on Scientific Computing.
Rapport
  • 2014. Integrators on homogeneous spaces: Isotropy choice and connections. .
  • 2014. B-series methods are exactly the local, affine equivariant methods. .
  • 2003. Generalized Polar Coordinates On Lie Groups And Numerical Integrators. 244. 244. .
  • 2002. On enumeration problems in Lie-Butcher theory. .
  • 2001. Application of symmetric spaces and Lie-triple systems in numerical analysis. 217. 217. .
  • 2000. The polar decomposition on Lie groups with involutive automorphisms. .
  • 2000. The polar decomposition on Lie groups with involutive automorphisms. .
  • 2000. Generalized polar decompositions for the approximation of the matrix exponential. .
  • 2000. Generalized polar decompositions for the approximation of the matrix exponential. .
  • 1999. Multistep Methods Integrating Ordinary Differential Equations on Manifolds. 3. 3. .
  • 1999. DiffMan, an object oriented MATLAB toolbox for solving differential equations on manifolds. 164. 164. .
  • 1999. DiffMan - User's Guide Version 1.6. 166. 166. .
  • 1999. Adjoint and selfadjoint Lie-group. 2. 2. .
  • 1998. Computations in a free Lie algebra. 148. 148. .
  • 1997. High Order Runge--Kutta Methods on Manifolds. NA14. NA14. .
  • 1994. Optimizing overloaded arithmetic operators in C++. 95. 95. .
  • 1994. Coordinate Free Numerics, Part 1. 101. 101. .
  • 1994. An algebraic theory fro regular mappings on parallel computers. 102. 102. .
  • 1994. 2D Prestack Migration on the MasPar MP-1. 93. 93. .
  • 1992. Generalized shuffle exchange networks. .
  • 1991. Super Parallel FFT's. .
  • 1991. Implementation of a SAR processing algorithm on MasPar MP-1208. .
  • 1991. Componentwise error analysis of FFT's with applicatons to fast Helmholz solvers. .
Faglig foredrag
  • 2014. Symmetries and reversing symmetries in differential equations and linear algebra.
Populærvitenskapelig foredrag
  • 1997. High order Runge-Kutta Methods on manifolds.
  • 1997. Geometrisk integrasjon av differensiallikninger, en innføring.
  • 1997. Coordinate free methods in scientific computing.
  • 1997. An introduction to Lie group methods.
  • 1994. Routing K-file permutations on parallel computers.
  • 1994. Coordinate free Numerics.
Vitenskapelig foredrag
  • 2015. Numerical integration, structure preservation and combinatorics (4 hrs lectures).
  • 2015. Groups and symmetries in numerical linear algebra (6 hours lectures).
  • 2015. Geometry and algebra of Buther- and Lie-Butcher series.
  • 2013. On post-Lie algebras, Lie-Butcher series and moving frames.
  • 2006. Volume preserving splitting methods for divergence free vector fields.
  • 2006. Explicit, volume preserving splitting methods for divergence-free polynomial vector fields.
  • 2006. Explicit volume preserving methods for divergence-free polynomial vector fields.
  • 2003. Numerical methods for the computation of exponential of matrices.
  • 2002. On the geometric exactness of Lie group integrators.
  • 2002. On equivariance of numerical integrators.
  • 2002. Introduction to Lie group integrators.
  • 2001. Lie group integrators based on generalized polar coordinates.
  • 2001. Lie group integrators based on generalized polar coordinates.
  • 2001. Canonical spherical integrators applied to PDEs.
  • 2000. On the Role of Mathematical Abstractions for Scientific Computing.
  • 2000. On the Role of Mathematical Abstractions for Scientific Computing.
  • 1997. Numerical Integration of Differential Equations on Homogeneous Manifolds.
  • 1997. Iterated Commutators, Lie's Reduction Method and Ordinary Differential Equations on Matrix Lie Groups.
  • 1994. Routing K-file permutations on parallel computers.
  • 1993. Solving tensor fields on parallel computers, applications to forward modelling.
  • 1993. Modelling waves in discontinuous media; Uniformly converging schemes.
  • 1992. Prestack Migration on a Massively Parallel Computer.
  • 1992. Algebraic Programming Technology for Partial Differential Equations.
  • 1991. Super Parallel FFT's with applications to Seismic Migration.
Leder
  • 2008. Guest Editors' Preface. Foundations of Computational Mathematics. 289-290.
Vitenskapelig antologi/Konferanseserie
  • 2018. Computation and Combinatorics in Dynamics, Stochastics and Control. Springer.
Kompendium
  • 1998. DiffMan - an object oriented MATLAB toolbox for solving differential equations on manifolds: User's Guide (preliminary version).
  • 1997. DiffMan - an object oriented MATLAB toolbox for solving differential equations on manifolds: User's Guide.
  • 1993. Practical parallel permutation procedures.
Intervju
  • 2018. Bergens nye attraksjon.
Vitenskapelig Kapittel/Artikkel/Konferanseartikkel
  • 2015. On algebraic structures of numerical integration on vector spaces and manifolds. 46 sider.
  • 1992. Generalized Shuffle Exchange Networks.
Errata
  • 2018. Correction to: On Post-Lie Algebras, Lie?Butcher Series and Moving Frames (Foundations of Computational Mathematics, (2013), 13, 4, (583-613), 10.1007/s10208-013-9167-7). Foundations of Computational Mathematics.
Vitenskapelig oversiktsartikkel/review
  • 2011. Topics in structure-preserving discretization. 1-119.

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Portrettfoto: Peter Badge ©. Spør meg om du vil bruke det, hans@math.uib.no.