Toward Scalable Non-Cartesian Computing

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The processing, analysis and visualization of large datasets are key challenges faced by the scientific computing community. Be it acquired imaging data or simulated computational fluid dynamics datasets, the scale and volume of these data are on the rise; experts are now planning for the era of exascale computing where supercomputers will be generating datasets in the order of exabytes (1 exabyte = 1 billion gigabytes). While computing performance continues to improve, our cognitive ability to make sense of this data explosion is certainly constant. There are also environmental factors we need to be wary of since large-scale computing applications consume massive amounts of energy. As we go forward, we will need to revisit our mathematical models and data management strategies so as to ensure that resources are optimally utilized. We will need to find a good balance between the data we can generate and the data we should generate so as to ensure that we can make sense of the data using limited computational and cognitive resources. ******The goal of this proposal is to tackle large data analysis and visualization challenges from the perspective of non-Cartesian computing. Non-Cartesian computing is inspired by nature and attempts to seek efficient data representations and algorithms that describe static and time-varying spatial phenomena. Nature is replete with instances of such representations; photoreceptors in the primate retina are arranged in a hexagonal fashion, sunflower seeds are packed in a spiral Fibonacci formation and our skin cells resemble a 14-sided polytope that tightly packs space. Yet, much of large-scale computing is done using the Cartesian grid that consists of cubic cells which are very inefficient at filling space. This inefficiency only worsens as problems are scaled up to larger sizes and higher dimensions. Switching to non-Cartesian representations offers a viable and attractive alternative as these representations promise the same fidelity as their Cartesian counterparts -- with significantly less computational cost. However, there are scalability challenges that need to be addressed before these representations can be used at peta and exa scales. This proposal therefore aims to investigate non-Cartesian data management and visualization algorithms that are specially designed for large-scale heterogeneous computing environments. Following the "do more with less" mantra, the ultimate goal is to offer simple and efficient data representation solutions that can be integrated into resource-constrained high performance computing and visualization workflows without sacrificing accuracy or performance.