Eigenpair extractions are crucial for various applications in geometry processing and graphics. State of the Art libraries like ARPACK or Spectra rely on the implicitly restarted Lanczos iteration to extract eigenpairs efficiently. However for some large scale problems they lack convergence speed and robustness. In this paper we present a simple multigrid extension to accelerate the convergence and robustness of the implicitly restarted Lanczos method, and we demonstrate the efficiency of our method on a variety of problems commonly found in geometry processing and graphics.

While discrete (metric) connections have become a staple of n -vector field design and analysis on simplicial meshes, the notion of torsion of a discrete connection has remained unstudied. This is all the more surprising as torsion is a crucial component in the fundamental theorem of Riemannian geometry, which introduces the existence and uniqueness of the Levi-Civita connection induced by the metric. In this paper, we extend the existing geometry processing toolbox by providing torsion control over discrete connections. Our approach consists in first introducing a new discrete Levi-Civita connection for a metric with locally-constant curvature to replace the hinge connection of a triangle mesh whose curvature is concentrated at singularities; from this reference connection, we define the discrete torsion of a connection to be the discrete dual 1-form by which a connection deviates from our discrete Levi-Civita connection. We discuss how the curvature and torsion of a discrete connection can then be controlled and assigned in a manner consistent with the continuous case. We also illustrate our approach through theoretical analysis and practical examples arising in vector and frame design.