PHAML

As a software reviewer, I must say that PHAML is an impressive project that achieves its primary goal of producing a parallel version of MGGHAT. The project has extended its capabilities to include additional features, making it a complete package for solving elliptic partial differential equations using low or high order finite elements, adaptive mesh refinement based on newest node bisection of triangles, and multigrid techniques.

PHAML is designed to work with distributed memory multiprocessors like Beowolf-type PC clusters. It is an attempt to combine the most effective means of vastly reducing the time required to solve differential equations, including adaptive refinement, multigrid, and parallel computing. The developers have done an excellent job of making this notoriously difficult task more accessible.

What's new in this release is impressive. PHAML now comes with features like quadrature rules of order 21 to 45 for triangles, a new parallel implementation of conjugate gradients, and the option for printing relative error instead of absolute error. Additionally, PHAML comes with a MUMPS non-symmetric solver, and vertical scaling in graphics has been improved. Double-precision floats are now used for graphics, and roundoff error has been reduced in computing barycentric coordinates.

Further, the quad order for elemental matrices has been increased to be exact for the mass matrix, and there have been various bugfixes, code cleanups, and speedups. All these new features make PHAML an even more powerful tool for solving elliptic partial differential equations.

In conclusion, PHAML is an excellent software package that delivers on its promises. It is an easy-to-use, effective, and powerful tool for solving differential equations. If you're looking for a software package to solve elliptic partial differential equations, PHAML is a great option that boasts the most effective means of solving these equations.