# Ratel: Extensible, performance-portable solid mechanics#

Ratel is a solid mechanics library and applications based on libCEED and PETSc with support for efficient high-order elements and CUDA and ROCm GPUs.

Solid mechanics simulations provide vital information for many engineering applications, using a large amount of computational resources from workstation to supercomputing scales. The industry standard for implicit analysis uses assembled sparse matrices with low-order elements, typically $$Q_1$$ hexahedral and $$P_2$$ tetrahedral elements, with the linear systems solved using sparse direct solvers, algebraic multigrid, or multilevel domain decomposition. This approach has two fundamental inefficiencies: poor approximation accuracy per Degree of Freedom (DoF) and high computational and memory cost per DoF due to choice of data structures and algorithms. High-order finite elements implemented in a matrix-free fashion with appropriate preconditioning strategies can overcome these inefficiencies.

For further details on the benefits of high-order, matrix-free finite elements for solid mechanics, see our preprint on arXiv.

# Indices and tables#

[DPA+20]

Denis Davydov, Jean-Paul Pelteret, Daniel Arndt, Martin Kronbichler, and Paul Steinmann. A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid. International Journal for Numerical Methods in Engineering, 121(13):2874–2895, 2020. doi:10.1002/nme.6336.

[Hol00]

Gerhard Holzapfel. Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester New York, 2000. ISBN 978-0-471-82319-3.

[NW99]

Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999.