# ManifoldCode

MC is a parallel adaptive multilevel finite element code developed by Michael Holst over a number of years, beginning in 1994. MC consists of about 100,000 lines of ”Clean Object C”, which is a dialect (a proper subset) of ANSI/ISO C. MC is designed to numerically approximate the solutions of covariant divergence-form second-order nonlinear elliptic systems of partial differential equations on domains with the structure of Riemannian two- and three-manifolds. To accomplish this task as accurately and efficiently as possible, MC employs simplex triangulations of the domain manifold, Petrov-Galerkin finite element methods, a posteriori error estimation, adaptive mesh refinement and un-refinement, continuation, Newton methods, multilevel methods, and a new low-communication approach in parallel adaptive finite element methods. MC was designed primarily to simulate the large deformation nonlinear elastic behavior of complicated hyperelastic bodies, although it can also be used for problems such as the nonlinear Poisson-Boltzmann equation arising in biophysics, the drift-diffusion semiconductor equations, and the Hamiltonian and momentum constraints in the Einstein equations. Ongoing projects include extending MC to numerically evolve the Ricci flow equations in Geometry and the full Einstein equations in relativity physics.

## References in zbMATH (referenced in 1 article , 1 standard article )

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