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Abstract Fractional PDEs have recently found several geophysics and imaging science applications due to their nonlocal nature and their flexibility in capturing sharp transitions across interfaces.However, this nonlocality makes it challenging to design efficient solvers for such problems.In this paper, we introduce a spectral method based on an ultraspherical polynomial discretization of the Caffarelli–Silvestre extension to solve such PDEs on rectangular and disk domains.We solve the discretized problem using tensor equation solvers and thus can solve higher-dimensional PDEs.In addition, we introduce both serial and parallel domain decomposition solvers.We demonstrate the numerical performance of our methods on a 3D fractional elliptic PDE on a cube as well as an application to optimization problems with fractional PDE constraints.more » « less
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Abstract The convergence of DFT‐computed interaction energies with increasing binding site model size was assessed. The data show that while accurate intercalator interaction energies can be derived from binding site models featuring only the flanking nucleotides for uncharged intercalators that bind parallel to the DNA base pairs, errors remain significant even when including distant nucleotides for intercalators that are charged, exhibit groove‐binding tails that engage in noncovalent interactions with distant nucleotides, or that bind perpendicular to the DNA base pairs. Consequently, binding site models that include at least three adjacent nucleotides are required to consistently predict converged binding energies. The computationally inexpensive HF‐3c method is shown to provide reliable interaction energies and can be routinely applied to such large models.
