Christian Lubich | Academic Influence

Christian Lubich's AcademicInfluence.com Rankings

Christian Lubich

Mathematics

#3287

World Rank

#4884

Historical Rank

Linear Algebra

#5

World Rank

#7

Historical Rank

Applied Mathematics

#67

World Rank

#79

Historical Rank

Measure Theory

#482

World Rank

#685

Historical Rank

mathematics Degrees

Download Badge

Mathematics

Christian Lubich's Degrees

PhD Mathematics University of Vienna

Why Is Christian Lubich Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Christian Lubich is an Austrian mathematician, specializing in numerical analysis. Education and career After secondary education at the Bundesrealgymnasium in Innsbruck, Lubich studied mathematics at the University of Innsbruck from 1977 to graduation with Magister degree in 1981. He was from 1979 to 1981 a student assistant in Innsbruck and from 1981 to 1983 a research associate in the Sonderforschungsbereich 123 Stochastische mathematische Modelle at the University of Heidelberg. He received his doctorate in 1983 from the University of Innsbruck with dissertation Zur Stabilität linearer Mehrschrittverfahren für Volterra-Gleichungen under Ernst Hairer and habilitated there in 1987. Lubich was from 1983 to 1987 a university assistant in Innsbruck, in 1986/87 an assistant at the University of Geneva, in 1987/88 a visiting professor at the IRMAR at the University of Rennes, and in 1988 a visiting professor at the University of Geneva. He was from 1991 to 1992 an assistant professor at ETH Zurich and from 1992 to 1994 a professor of applied mathematics at University of Würzburg. He is since 1994 a professor of numerical mathematics at the University of Tübingen.

(See a Problem?)

Christian Lubich's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations (2004) (3512)
Geometric Numerical Integration (2022) (1060)
Discretized fractional calculus (1986) (853)
On Krylov Subspace Approximations to the Matrix Exponential Operator (1997) (813)
The numerical solution of differential-algebraic systems by Runge-Kutta methods (1989) (724)
Convolution quadrature and discretized operational calculus. II (1988) (611)
Geometric numerical integration illustrated by the Störmer–Verlet method (2003) (555)
Convolution quadrature and discretized operational calculus. I (1988) (546)
Exponential Integrators for Large Systems of Differential Equations (1998) (542)
From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis (2008) (394)
Unifying time evolution and optimization with matrix product states (2014) (346)
On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations (2008) (311)
Error Bounds for Exponential Operator Splittings (2000) (275)
Convolution quadrature time discretization of fractional diffusion-wave equations (2006) (252)
On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations (1994) (248)
A Gautschi-type method for oscillatory second-order differential equations (1999) (245)
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations (2000) (241)
Dynamical Low-Rank Approximation (2007) (222)
Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term (1996) (212)
Fractional linear multistep methods for Abel-Volterra integral equations of the second kind (1985) (200)
The life-span of backward error analysis for numerical integrators (1997) (194)
Fast Convolution for Nonreflecting Boundary Conditions (2002) (193)
RUNGE-KUTTA METHODS FOR PARABOLIC EQUATIONS AND CONVOLUTION QUADRATURE (1993) (176)
Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets (2009) (173)
FAST NUMERICAL SOLUTION OF NONLINEAR VOLTERRA CONVOLUTION EQUATIONS (1985) (171)
Multi-grid dynamic iteration for parabolic equations (1987) (169)
Convolution Quadrature Revisited (2004) (158)
Fast and Oblivious Convolution Quadrature (2005) (158)
Dynamical Approximation by Hierarchical Tucker and Tensor-Train Tensors (2013) (154)
Runge-Kutta theory for Volterra and Abel integral equations of the second kind (1983) (138)
Time Integration of Tensor Trains (2014) (132)
A projector-splitting integrator for dynamical low-rank approximation (2013) (129)
Conservation of energy, momentum and actions in numerical discretizations of non-linear wave equations (2008) (123)
Structure-Preserving Algorithms for Ordinary Differential Equations (2006) (121)
On Magnus Integrators for Time-Dependent Schrödinger Equations (2003) (121)
Runge-Kutta approximation of quasi-linear parabolic equations (1995) (116)
Dynamical Tensor Approximation (2010) (114)
On the Stability of Linear Multistep Methods for Volterra Convolution Equations (1983) (112)
Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations (1988) (103)
Linearly implicit time discretization of non-linear parabolic equations (1995) (101)
An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics (2010) (100)
Runge–Kutta convolution quadrature for operators arising in wave propagation (2011) (95)
Operator splitting for partial differential equations with Burgers nonlinearity (2011) (95)
The Mystery of Antibodies Against Polyethylene Glycol (PEG) - What do we Know? (2016) (94)
Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory (2006) (84)
A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral Equations (1986) (83)
Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times (2010) (82)
Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review (2006) (82)
Exponential Integrators for Quantum-Classical Molecular Dynamics (1999) (80)
On resolvent conditions and stability estimates (1991) (79)
Extrapolation integrators for constrained multibody systems (1991) (78)
Time discretization of parabolic boundary integral equations (1992) (77)
Backward difference time discretization of parabolic differential equations on evolving surfaces (2013) (77)
Numerical Energy Conservation for Multi-Frequency Oscillatory Differential Equations (2005) (74)
Multirate extrapolation methods for differential equations with different time scales (1997) (72)
Modulated Fourier Expansions of Highly Oscillatory Differential Equations (2003) (72)
Integration of stiff mechanical systems by Runge-Kutta methods (1993) (70)
Energy-diminishing integration of gradient systems (2014) (64)
Long-Time Analysis of Nonlinearly Perturbed Wave Equations Via Modulated Fourier Expansions (2008) (64)
Symmetric multistep methods over long times (2004) (63)
Stable numerical coupling of exterior and interior problems for the wave equation (2013) (63)
An error analysis of Runge–Kutta convolution quadrature (2011) (63)
CD4+ T-cell epitopes associated with antibody responses after intravenously and subcutaneously applied human FVIII in humanized hemophilic E17 HLA-DRB1*1501 mice. (2012) (61)
Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values (2016) (60)
Fast numerical solution of weakly singular Volterra integral equations (1988) (59)
Fully implicit, linearly implicit and implicit–explicit backward difference formulae for quasi-linear parabolic equations (2015) (58)
On variational approximations in quantum molecular dynamics (2004) (57)
On the stability of semi-implicit methods for ordinary differential equations (1982) (56)
Nonlinear Schrödinger Equations and Their Spectral Semi-Discretizations Over Long Times (2010) (55)
Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations (2016) (55)
Sobolev Stability of Plane Wave Solutions to the Cubic Nonlinear Schrödinger Equation on a Torus (2011) (53)
On the convergence of multistep methods for nonlinear stiff differential equations (1992) (52)
A-Stable Time Discretizations Preserve Maximal Parabolic Regularity (2015) (52)
Runge–Kutta time discretization of parabolic differential equations on evolving surfaces (2012) (50)
Computing quantum dynamics in the semiclassical regime (2020) (50)
Time Integration in the Multiconfiguration Time-Dependent Hartree Method of Molecular Quantum Dynamics (2015) (49)
Low-Rank Dynamics for Computing Extremal Points of Real Pseudospectra (2013) (47)
Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: nonsmooth-data error estimates and applications to long-time behaviour (1996) (47)
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces (2018) (46)
A Poisson Integrator for Gaussian Wavepacket Dynamics (2006) (46)
Dynamical low-rank approximation: applications and numerical experiments (2008) (44)
Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the First Kind (1987) (43)
A Low-Rank Projector-Splitting Integrator for the Vlasov-Poisson Equation (2018) (43)
Order of Convergence of One-Step Methods for Volterra Integral Equations of the Second Kind (1983) (42)
Adiabatic Integrators for Highly Oscillatory Second-Order Linear Differential Equations with Time-Varying Eigendecomposition (2005) (42)
Differential Equations for Roaming Pseudospectra: Paths to Extremal Points and Boundary Tracking (2011) (42)
A variational splitting integrator for quantum molecular dynamics (2004) (41)
Asymptotic expansions of the global error of fixed-stepsize methods (1984) (41)
Spectral Semi-discretisations of Weakly Non-linear Wave Equations over Long Times (2008) (39)
Symmetric multistep methods for charged-particle dynamics (2017) (38)
Numerical Integration of Constrained Mechanical Systems Using MEXX (1995) (37)
Error Analysis of Krylov Methods In a Nutshell (1998) (36)
Energy behaviour of the Boris method for charged-particle dynamics (2018) (36)
On convolution quadrature and Hille-Phillips operational calculus (1992) (36)
Numerical integrators for quantum dynamics close to the adiabatic limit (2003) (35)
Fast Runge-Kutta approximation of inhomogeneous parabolic equations (2005) (35)
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field (2019) (34)
Runge-Kutta theory for Volterra integrodifferential equations (1982) (34)
An unconventional robust integrator for dynamical low-rank approximation (2020) (33)
Low rank differential equations for Hamiltonian matrix nearness problems (2015) (33)
Numerical analysis of parabolic problems with dynamic boundary conditions (2015) (33)
Interior estimates for time discretizations of parabolic equations (1995) (33)
Long-term analysis of the Störmer–Verlet method for Hamiltonian systems with a solution-dependent high frequency (2016) (31)
PLANE WAVE STABILITY OF THE SPLIT-STEP FOURIER METHOD FOR THE NONLINEAR SCHRÖDINGER EQUATION (2013) (30)
Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics (2007) (30)
Convergence of finite elements on an evolving surface driven by diffusion on the surface (2016) (29)
h2-Extrapolation methods for differential-algebraic systems of index 2 (1989) (29)
Time Integration of Rank-Constrained Tucker Tensors (2017) (29)
MUR8: a multirate extension of the eighth-order Dormand-Prince method (1997) (28)
Linearly implicit extrapolation methods for differential-algebraic systems (1989) (28)
Periodic orbits of delay differential equations under discretization (1998) (28)
Symplectic integration of post-Newtonian equations of motion with spin (2010) (28)
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field (2020) (28)
Implementation of a novel projector-splitting integrator for the multi-configurational time-dependent Hartree approach. (2017) (27)
On the Energy Distribution in Fermi–Pasta–Ulam Lattices (2012) (26)
Extrapolation at stiff differential equations (1988) (26)
Rosenbrock methods for differential-algebraic systems with solution-dependent singular matrix multiplying the derivative (1990) (26)
Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity (2016) (25)
A rank-adaptive robust integrator for dynamical low-rank approximation (2021) (25)
On the Nearest Singular Matrix Pencil (2017) (25)
A Quasi-Conservative Dynamical Low-Rank Algorithm for the Vlasov Equation (2018) (24)
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions (2014) (23)
On projected Runge-Kutta methods for differential-algebraic equations (1991) (23)
Variational discretization of wave equations on evolving surfaces (2014) (22)
Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers (2009) (21)
A Bunch of Time Integrators for Quantum/Classical Molecular Dynamics (1999) (20)
Acta Numerica 2003: Geometric numerical integration illustrated by the Störmer–Verlet method (2003) (20)
Variational-splitting time integration of the multi-configuration time-dependent Hartree–Fock equations in electron dynamics (2011) (20)
Oscillations over long times in numerical Hamiltonian systems (2009) (20)
Energy Separation in Oscillatory Hamiltonian Systems without any Non-resonance Condition (2012) (19)
Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization (1999) (19)
On the Stability of Volterra–Runge–Kutta Methods (1984) (18)
A convergent evolving finite element algorithm for Willmore flow of closed surfaces (2020) (18)
Matrix Stabilization Using Differential Equations (2017) (17)
Energy conservation by Stoermer-type numerical integrators (2000) (16)
Modulated Fourier Expansions for Continuous and Discrete Oscillatory Systems (2012) (16)
Higher-order linearly implicit full discretization of the Landau-Lifshitz-Gilbert equation (2019) (15)
Integrators for quantum dynamics : a numerical analyst ’ s brief review (2002) (15)
Uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line (1991) (15)
Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type (2016) (15)
Time integration of tree tensor networks (2020) (15)
Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization (1998) (15)
Linearly implicit full discretization of surface evolution (2017) (14)
DYNAMICS, NUMERICAL ANALYSIS, AND SOME GEOMETRY (2017) (14)
Asymptotic expansions and backward analysis for numerical integrators (2000) (14)
Runge-Kutta solutions of stiff differential equations near stationary points (1995) (14)
Metastable Energy Strata in Weakly Nonlinear Wave Equations (2012) (12)
OPERATIONAL QUADRATURE METHODS FOR WIENER-HOPF INTEGRAL EQUATIONS (1993) (12)
Symmetric multistep methods for constrained Hamiltonian systems (2013) (12)
Free and constrained symplectic integrators for numerical general relativity (2008) (11)
A convergent algorithm for forced mean curvature flow driven by diffusion on the surface (2020) (11)
Chebyshev acceleration of picard-lindelöf iteration (1992) (11)
A convergent algorithm for forced mean curvature flow driven by diffusion on the surface (2020) (11)
Runge-Kutta methods for differential-algebraic equations (1989) (11)
Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations (2016) (11)
Long-term analysis of semilinear wave equations with slowly varying wave speed (2016) (10)
An overview of MEXX: Numerical Software for the Integration of Multibody Systems (1993) (10)
Hamiltonian Perturbation Theory and Symplectic Integrators (2006) (9)
A Flow-Cytometry-Based Approach to Facilitate Quantification, Size Estimation and Characterization of Sub-visible Particles in Protein Solutions (2015) (9)
Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors (2019) (9)
Runge–Kutta convolution coercivity and its use for time-dependent boundary integral equations (2017) (9)
Inertial manifolds of parabolic differential equations under high-order discretizations (1999) (9)
Erratum/Addendum: Differential Equations for Roaming Pseudospectra: Paths to Extremal Points and Boundary Tracking (2012) (7)
Modulation of the liver immune microenvironment by the adeno-associated virus serotype 8 gene therapy vector (2020) (7)
Error of rosenbrock methods for stiff problems studied via differential algebraic equations (1989) (7)
Large-stepsize integrators for charged-particle dynamics over multiple time scales (2021) (7)
VARIATIONAL DISCRETIZATION OF LINEAR WAVE EQUATIONS ON EVOLVING SURFACES (2012) (7)
Long-term control of oscillations in differential equations (2013) (7)
On the convergence of multistep methods for nonlinear stiff differential equations (1990) (6)
On Dynamics and Bifurcations of Nonlinear Evolution Equations Under Numerical Discretization (2001) (6)
Comparative analysis of marketed factor VIII products: recombinant products are not alike vis‐a‐vis soluble protein aggregates and subvisible particles (2018) (6)
Measuring the stability of spectral clustering (2019) (6)
Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature (2020) (5)
Rank-adaptive time integration of tree tensor networks (2022) (5)
Computing Extremal Points of Symplectic Pseudospectra and Solving Symplectic Matrix Nearness Problems (2014) (5)
Fast Numerical Solution of Singular Integral Equations (1994) (4)
Constrained Graph Partitioning via Matrix Differential Equations (2019) (4)
Convergence of finite elements on a solution-driven evolving surface (2016) (4)
Interior a posteriori error estimates for time discrete approximations of parabolic problems (2013) (4)
Numerical Integrators for Motion under a Strong Constraining Force (2014) (3)
Finding the Nearest Passive or Nonpassive System via Hamiltonian Eigenvalue Optimization (2021) (3)
Structure-Preserving Implementation (2006) (3)
Description of differential-algebraic problems (1989) (3)
Symplectic Integration of Hamiltonian Systems (2006) (3)
Featured Review: Geometric Numerical Integration: Structure-Preserving Al (2016) (2)
Backward Error Analysis and Structure Preservation (2006) (2)
Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations (2021) (2)
Low-Rank Dynamics (2014) (2)
Order conditions of Runge-Kutta methods for index 2 systems (1989) (2)
A convergent algorithm for mean curvature flow driven by diffusion on the surface (2019) (2)
Time-dependent electromagnetic scattering from thin layers (2021) (2)
Highly Oscillatory Differential Equations (2002) (2)
Analysis and Time Integration of the Multi-Conflguration Time-Dependent Hartree-Fock Equations in Electronic Dynamics (2008) (2)
Graph partitioning using matrix differential equations (2017) (1)
Convergence for index 3 problems (1989) (1)
Rank-1 matrix differential equations for structured eigenvalue optimization (2022) (1)
Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations (2017) (1)
Examples of differential-algebraic systems and their solution (1989) (1)
Numerical solution of ordinary differential equations (2010) (1)
Convergence for index 1 problems (1989) (1)
Stable numerical coupling of exterior and interior problems for the wave equation (2014) (1)
Symmetric Integration and Reversibility (2006) (1)
Convergence for index 2 problems (1989) (1)
Dynamics of Multistep Methods (2006) (1)
Local error estimation (1989) (1)
Low rank differential equations for Hamiltonian matrix nearness problems (2014) (1)
are all marketed Fviii products the same? Comparative analysis of important quality parameters of Fviii products (2016) (1)
Order Conditions, Trees and B-Series (2006) (1)
On a large-stepsize integrator for charged-particle dynamics (2022) (1)
hemophilic E17 HLA-DRB1*1501 mice intravenously and subcutaneously applied human FVIII in humanized T-cell epitopes associated with antibody responses after + CD4 (2012) (0)
Numerical simulations of long-range open quantum many-body dynamics with tree tensor networks (2023) (0)
Leapfrog methods for relativistic charged-particle dynamics (2023) (0)
Interior a posteriori error estimates for time discrete approximations of parabolic problems (2013) (0)
Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions (2014) (0)
Dissipatively Perturbed Hamiltonian and Reversible Systems (2006) (0)
Non-Canonical Hamiltonian Systems (2006) (0)
Stability and convergence of time discretizations of quasi-linear evolution equations of Kato type (2017) (0)
A passivation algorithm for linear time-invariant systems (2020) (0)
EXPONENTIAL INTEGRATORS FORQUANTUM-CLASSICAL MOLECULAR DYNAMICSMARLIS (2010) (0)
Energy behaviour of the Boris method for charged-particle dynamics (2018) (0)
A Flow-Cytometry-Based Approach to Facilitate Quantification, Size Estimation and Characterization of Sub-visible Particles in Protein Solutions (2015) (0)
Further Topics in Structure Preservation (2002) (0)
Reversible Perturbation Theory and Symmetric Integrators (2006) (0)
Linearly implicit full discretization of surface evolution (2018) (0)
A filtered Boris algorithm for charged-particle dynamics in a strong magnetic field (2020) (0)
Book reviews (1992) (0)
Polarized high-frequency wave propagation beyond the nonlinear Schr\"odinger approximation (2022) (0)
A parallel rank-adaptive integrator for dynamical low-rank approximation (2023) (0)
Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations (2021) (0)
Anti-PEG antibodies in experimental animal disease models and in patients treated with PEGylated proteins (2008) (0)
On the Energy Distribution in Fermi–Pasta–Ulam Lattices (2012) (0)
Runge–Kutta Time Discretization of Nonlinear Parabolic Equations Studied via Discrete Maximal Parabolic Regularity (2017) (0)
Numerical periodic orbits of neutral delay differential equations (2005) (0)
Computational and Numerical Analysis of Transient Problems in Acoustics, Elasticity, and Electromagnetism (16w5071) (2016) (0)
Energy Separation in Oscillatory Hamiltonian Systems without any Non-resonance Condition (2013) (0)
An unconventional robust integrator for dynamical low-rank approximation (2021) (0)
Induction and Break of Immune Tolerance to Human FVIII in a HLA-DRB1*1501 Humanized Hemophilic Mouse Model (2011) (0)
Conservation of First Integrals and Methods on Manifolds (2006) (0)
N A ] 2 1 A ug 2 02 0 TIME INTEGRATION OF TREE TENSOR NETWORKS (2020) (0)
ANU volume 29 Cover and Front matter (2020) (0)
Examples and Numerical Experiments (2006) (0)
Oscillatory Differential Equations with Constant High Frequencies (2006) (0)
Modulating the microenvironment during FVIII uptake influences the nature of FVIII-peptides presented by antigen-presenting cells (2022) (0)
Convergence of finite elements on an evolving surface driven by diffusion on the surface (2017) (0)
On the MCTDH method (2013) (0)
Naturally Occurring Regulatory T Cells Modulate Immune Responses Against Exogenous Factor VIII in Hemophilic Balb/c Mice but Not in C57BL/6J Mice. (2007) (0)
and Discretized Operational Calculus. II (1988) (0)
Solution of nonlinear systems by simplified Newton (1989) (0)
Fully implicit, linearly implicit and implicit–explicit backward difference formulae for quasi-linear parabolic equations (2015) (0)
Symmetric multistep methods for constrained Hamiltonian systems (2013) (0)
The Mystery of Antibodies Against Polyethylene Glycol (PEG) - What do we Know? (2016) (0)
Long-time-step methods for oscillatory Hamiltonian systems (2007) (0)
Preclinical Immunogenicity Assessment of Baxter‘s Longer-Acting FVIII Candidate BAX 855 Using Novel Preclinical Models, (2011) (0)
Oscillatory Differential Equations with Varying High Frequencies (2006) (0)
Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors (2020) (0)
A projector-splitting integrator for dynamical low-rank approximation (2013) (0)
Long-term analysis of the Störmer–Verlet method for Hamiltonian systems with a solution-dependent high frequency (2015) (0)
Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field (2020) (0)
Symplectic Integrators for General Relativity (2007) (0)
Semiclassical Wave Packets on Riemannian Manifolds (2017) (0)

This paper list is powered by the following services:

Other Resources About Christian Lubich

en.wikipedia.org

What Schools Are Affiliated With Christian Lubich?

Christian Lubich is affiliated with the following schools:

Image Attributions

Image Source for Christian Lubich