As with any research effort, one is required to decide on a set of guiding principles that will drive the investigation. Similarly with a software development effort of this form, we spent considerable time early on considering which aspects we wanted to be distinctive about Nektar++ and also what guiding principles would be most suitable to support both the goals and the boundaries of what we wanted to do. We did this for at least two reasons: (1) We acknowledged then and now that there are various software packages and open-source efforts that deal with finite element frameworks, and so we wanted to be able to understand and express to people those things we thought were distinctive to us – that is, our “selling points”. (2) We also acknowledged, from our own experience on software projects, that if we did not set up some collection of guiding principles for our work, that we would gravitate towards trying to be “all things to all men", and in doing so be at odds with the first item. Below are a list of the guiding principles, the “ethos”, of the Nektar++ software development effort.
Principles: The following are our three guiding principles for Nektar++ which respect (1) above:
Efficiently: Nektar++ was to be a “true” high-order code. “True” is put in quotations because we acknowledge that high-order means different things to different communities. Based upon a review of the literature, we came to the conclusion that part of our h-to-p philosophy should be that we accommodate polynomial degrees ranging from zero (finite volumes) or one (traditional linear finite elements) up to what is considered “spectral” (pseudospectral) orders of 16^{th} degree. As part of our early work [68], we established that in order to span this range of polynomial degrees and attempt to maintain some level of computational efficiency, we would need to develop order-aware algorithms: that is, we would need to utilize different (equivalent) algorithms appropriate for a particular order. This principle was the starting point of our h-to-p efficiently branding and continues to be a driving principle of our work.
Transparently: Nektar++ was to be agnostic as to what the “right” way to discretize a partial differential equation (PDE). “Right” is put in quotations to acknowledge that like the issue of polynomial order, there appear to be different “camps” who hold very strong views as to which discretization method should be used. Some might concede that continuous Galerkin methods are very natural for elliptic and parabolic PDEs and then work very laboriously to shoehorn all mixed-type PDEs (such as the incompressible Navier-Stokes equations) into this form. This holds true (similarly) for finite volume and dG proponents with regards to hyperbolic problems (and those systems that are dominated by hyperbolicity). Our goal was to be a high-order finite element framework that allowed users to experiment with continuous Galerkin (cG) and discontinuous Galerkin (dG) methods. After our original developments, we incorporated Flux-Reconstruction Methods (FR Methods) into our framework; this confirmed that generality of our approach as our underlying library components merely needed new features added to accommodate the FR perspective on dG methods. As stated earlier, this is in part why we use the term spectral/hp as it allows us to capture all these various methods (e.g., cG, dG and FR) under one common element-and-order terminology.
Seamlessly: Nektar++ was to be a code that could run from the desktop (or laptop) to exascale, seamlessly. It was our observation that many grand challenge efforts target petascale and exascale computing, with the idea that in the future what is done now on a supercomputer will be done on the desktop. The supercomputer of today is in a rack within five years and on our desktop in ten years. However, we also acknowledged that many of our end users were interested in computing now. That is, following from their engineering tradition they had an engineering or science problem to solve, and they wanted the ability to run on machines ranging from their laptops to exascale as the problem demanded. Not all problems fit on your laptop, and yet not all problems are exascale problems. Like with our h-to-p efficiently approach, we wanted our algorithms and code development to allow a range of choices in the hands of the engineer.
Based upon these principles, our long-term vision is a software framework that allows the engineer the flexibility to make all these critical choices (elemental discretization, polynomial order, discretization methodology, algorithms to employ, and architecture-specific details) while at the same time having smart and adaptive defaults. That is, we want to accommodate both the engineer that wants control over all the various knobs that must be set to actualize a simulation run and the engineer that wants to remain at the high-level and let the software system choose what is best in terms of discretization, polynomial order, algorithm choice, etc. We want the flexibility to self tune, while targeting auto-tuning.
The three items above denote the principles of our development efforts. We now present the “guardrails”. By guardrails, we mean the guidelines we use to help steer us along towards our goal as stated above. These are not meant to be absolutes necessarily, but are considerations we often use to try to keep us on track in terms of respecting our three guiding principles above.
We are principally concerned with advection-reaction-diffusion and conservation law problems. There are many simulation codes that are deal with solid mechanics, and we did not see ourselves as being a competitor with them. As such, we did not initially construct our framework to inherently deal with H - div and H - curl spaces (and their respective element types). Our perspective was to hold a system of scalar fields and, as needed, constrain them to respect certain mathematical properties.
We rely heavily on the ability to do tensor-product-based quadrature. Although our more recent additions to the Point and Basis information within our library allows for unstructured quadrature, many of our algorithms are designed to try to capitalize on tensor-product properties.
As we said earlier, we have designed our code to run at a range of orders, from one to sixteen. However, we acknowledge that for many simulation regimes, we often do not run at the lowest and/or the highest orders. For many applications, the sweet spot seems to be polynomials of degree four through eight. At the present time, a reasonable amount of time and effort has been spent optimizing for this range.
The robustness of our testing is often dictated by the application areas that have funded our code development. At the present time, our incompressible Navier-Stokes solver is probably the most tested of our solvers, followed by our ADR solver. We make every attempt to test our codes thoroughly; however we benefit greatly from various users “stress-testing” our codes and providing feedback on things we can improve (or better yet, suggesting coding solutions).