• Adaptive energy preserving methods for partial differential equations 

      Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article; Peer reviewed, 2017)
      A framework for constructing integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The approach can be used with both finite difference and partition of ...
    • Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows 

      Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article; Peer reviewed, 2018)
      This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative ordinary differential equations. This ...
    • Energy preserving methods on Riemannian manifolds 

      Celledoni, Elena; Eidnes, Sølve; Owren, Brynjulf; Ringholm, Torbjørn (Journal article, 2018)
      The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. ...
    • Integral Preserving Numerical Methods on Moving Grids 

      Eidnes, Sølve (Master thesis, 2013)
      Integral preservation for ordinary and partial differential equations is defined, and the integral preserving discrete gradient methods and discrete variational derivative methods on fixed grids are given, with a formal ...
    • Invariant-preserving integrators for differential equations 

      Eidnes, Sølve (Doctoral theses at NTNU;2020:166, Doctoral thesis, 2020)
    • Linearly implicit local and global energy-preserving methods for Hamiltonian PDEs 

      Eidnes, Sølve; Li, Lu (Journal article, 2019)
      We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods are tested on the one-dimensional Korteweg–de ...
    • Linearly implicit structure-preserving schemes for Hamiltonian systems 

      Eidnes, Sølve; Li, Lu; Sato, Shun (Journal article, 2019)
      Kahan’s method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a cubic Hamiltonian. These methods are here ...
    • Shape analysis on homogeneous spaces: a generalised SRVT framework 

      Celledoni, Elena; Eidnes, Sølve; Schmeding, Alexander (Chapter, 2017)
      Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of ...
    • Shape analysis on lie groups and homogeneous spaces 

      Celledoni, Elena; Eidnes, Sølve; Eslitzbichler, Markus; Schmeding, Alexander (Journal article, 2017)
      In this paper we are concerned with the approach to shape analysis based on the so called Square Root Velocity Transform (SRVT). We propose a generalisation of the SRVT from Euclidean spaces to shape spaces of curves on ...