Summer of Code Summary

During the summer, I contributed to multiple repositories under the JuliaDiffEq organization and completed the implementation of Exponential Runge-Kutta (ExpRK) integrators. My work can be roughly summarized into three parts: the exponential utilities, the integrators and sparse Jacobian support.

Exponential Utilities

The development of utility functions/types used by the exponential occurs on the first four weeks and is summarized by the following blog posts:

• Week 1 and 2
• Week 3 and 4

Near the end of GSoC, I also migrated the utilities to a separate package ExponentialUtilities under JuliaDiffEq.

Merged Pull Requests

OrdinaryDiffEq:

• Exponential utilities - phi functions #355
• Rewriting phimv and arnoldi #361
• Happy-breakdown detection and t parameter for phimv #365
• Lanczos algorithm for symmetric/Hermitian matrices #370
• Additional functionalities for exp utility: error estimate and IOP #372
• Krylov Phiv internal time stepping #375
• Adaptation for phiv_timestep(!) #376
• Time-stepping Krylov: special case for expv_timestep #378
• Packaged cache type for expv and phiv #408

Issues and Discussions

OrdinaryDiffEq:

• Adaptive Krylov exponential integrators (EPIRK) #243
• expmv and phimv performance #366

ExpRK Integrators

I implemented the infrastructure for the ExpRK integrators and wrote most of the algorithms during week 5 to 8. The adaptive Exponential Rosenbrock methods were added on week 12 and I plan to also add the SETD1 method for StochasticDiffEq after GSoC. Blog posts for this period:

• Week 5 and 6
• Week 6 and 7

Merged Pull Requrests

DiffEqBase:

• Update arguments style for DiffEqFunction #108
• Better in-place detection for DiffEqFunction #111

OrdinaryDiffEq:

• ETDRK integrators #385
• Hochbruck-Ostermann Method #395
• Optimizing the classical ExpRK integrators #401
• Exp4 using EPIRK #406
• Fourth order EPIRK methods #410
• Fifth order EPIRK methods #417
• Adaptive exponential Rosenbrock integrators #463

DiffEqDevDocs:

• ExpRK algorithm development guide #9

WIP Pull Requests

OrdinaryDiffEq:

• Update ExpRK alongside ExponentialUtilities #472

DiffEqDocs:

• Update ExpRK documentation #144

Issues and Discussions

OrdinaryDiffEq:

• Designing the exponential integrators #379
• Full list of exponential integrators to implement #394

Sparse Jacobian Support & Lazy W Operator

This started as an attempt to add sparse Jacobian support for the ExpRK integrators and ended up with a systematic improvement of the implicit handling functionality of JuliaDiffEq. I also helped upgrading JuliaDiffEq to v0.7 during this period. Blog post for this period:

• Week 9 through 12

Merged Pull Requests

DiffEqBase:

• Update handling of jac_prototype #123
• Mass matrix change #126

OrdinaryDiffEq:

• Update ExpRK to use calc_J! and new DiffEqOperators #438
• Lazy W operator support #443

DiffEqOperators:

• size(A, n) hotfix for array operator #66
• Basic operator composition #67

StochasticDiffEq:

• Update implicit methods to use lazy W #96

Minor PRs for v0.7 update:

• DiffEqBase: #124, #129
• OrdinaryDiffEq: #424, #455, #460. #461
• StochasticDiffEq: #93
• DiffEqOperators: #69
• DiffEqProblemLibrary: #31