Scalable paradigms and software for exascale scientific computing

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For the past three decades, high-performance computing (HPC) has profoundly contributed toward overcoming some of society's greatest challenges, including climate modelling, food and water security, and gene sequencing. HPC applications are core to Canada's identified sectors of innovation expertise and include large-scale simulations of hydrological flows, electrical activity in myocardial tissue, fluidized beds, and plasmas. These systems are modelled by partial differential equations (PDEs) that typically have disperate time scales and physical bases. Accordingly, no single time-integration method is able to effectively handle them all. To address this difficulty, we propose the use of high-order operator-splitting strategies combined with the design of optimized time-integration methods such as Runge-Kutta methods. HPC programming is largely based on the Message Passing Interface (MPI) library. Computing architectures and software requirements, however, have evolved considerably since then, whereas MPI has mostly remained static. In order to reap the full benefits of exascale computing, this research program also proposes to advance HPC programming beyond the MPI model through novel applications of concurrent programming, allowing many new and exciting research directions to be pursued that would otherwise remain intractable. The scope of such computations requires the software be fault tolerant. Although isolated faults are rare, the sheer number of components required means the chance of a fault occurring during a computation is non-negligible. In contrast to MPI, concurrent programming paradigms such as actors provide built-in fault tolerance. Actors can also elegantly handle faults by creating a minimum physical separation between redundant computations or by starting up new processes to replace faulty ones, eliminating the need for costly allocation of potentially wasted compute resources. Furthermore, both data parallelism and functional parallelism are required to fully exploit potential concurrency in a distributed HPC environment. MPI can handle data parallelism well. Management of functional parallelism, however, is generally highly problematic, both in terms of programming and computational efficiency. In this case, the run-time environments of actors can manage the creation, behaviour, and migration of actors to adeptly handle functional parallelism, leading to natural and low-cost programming and communication. The proposed research will enable more effective utilization of HPC resources in applications that involve the time integration of PDEs. This research will also produce significant software that will be made open source. I am in a unique and privileged position to lead fundamental research in the advancement of exascale scientific computing through the application of modern concurrency programming paradigms as well as to train the next generation of computational scientists in the post-MPI paradigm of HPC.