# Prelim Invite email

Subject: Request to be a part of my Thesis Committee
To: [e-mail]

Hello David,

I am nearing the end of my doctoral program and would like to invite you
to be a part of my Thesis committee. UIUC requires an external examiner to
be present on the committee and given your expertise in building systems
like Firedrake/TSFC and FEM in large, your feedback would be of great
value. I hope you can be a part of it.

I have outlined the main sections of my thesis and provided a rough
timeline until the final examination. 

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## Thesis Overview

The title of my Thesis is "Just-in-time Compilation Techniques for
Near-roofline Finite Element Systems" and the primary problems it
addresses are:
- How to optimize Finite-Element computational kernels lowered from the
Unified Form Language (UFL) for GPUs?
  - For a given operator, we prescribed a transformation space to achieve
  different levels of scratchpad memory usage and per-workgroup
  synchronization overheads.
  - We proposed a cost-model-based auto-tuning approach to arrive at the
  tuned kernel in the transformation space.
  - We proposed this as an optimization pass in the UFL-compiler Firedrake
  and demonstrated that our approach yields at least 50%-roofline
  performance for 70% of the kernels in the benchmark suite across
  multiple Nvidia micro-architectures.
  - A draft of the paper that we intend to submit to the Journal of
  Computational Physics soon:
  <https://uofi.box.com/s/fcdcc19ljoh4u3r1r83disoy4skq0rqf>

- How to build a Discontinuous-Galerkin FEM (DG-FEM) system with only
NumPy-like code?
  - We propose a lazy evaluation array framework based on Pytato
  <https://github.com/inducer/pytato> to capture the computation graph
  along with inter-rank communication.
  - This computation graph can be targeted to Loopy IR in which
  domain-specific transformations are applied.
  - We use this compilation pipeline to drive the production simulations
  in the MIRGE-Com project <https://mirgecom.readthedocs.io>.
  - Publication in preparation.

- What is a suitable kernel-fusion granularity for engineering a
near-roofline DG-FEM application?
  - We propose the kernel granularity of a Fused Einstein-Summation that
  describes a class of subprograms with the same summation expressions.
  - We also propose and develop a catalog of transformation for these
  subprograms.
  - We evaluated this approach on a suite of real-world applications like
  Wave equation, Maxwell's equations, and compressible Navier Stokes with
  chemistry terms. For these operators, we see ~50%-roofline performance,
  and equivalently a 3-5x speedup over state-of-the-art lazy evaluation
  array package JAX.
  - Publication in preparation.

## Timeline

The (tentative) timeline for the completion of the degree is as follows:
- Mid-to-late Nov 2022: I will send the Thesis committee my Prelim
document. It will be a 20-page document that will outline the work done
until now and what I propose to do till the Defense.
- Dec 7th 2022: Preliminary Examination. A 45 minutes presentation in
front of the Thesis committee followed by questions. This will be a closed
meeting at which only the committee members will be present.
- Start of June 2023: I will send the Thesis draft to the committee.
- End of June 2023: Defense Examination. A 45-minute presentation in front
of the Thesis committee that is open to UIUC students.
- The presentations would be conducted in an online/in-person hybrid
format.
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Thank you for considering the request.


Thanks,
Kaushik Kulkarni
<https://kaushikcfd.github.io/>