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In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive definite, thus the preconditioning conjugate gradient or the…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
The sheer sizes of modern datasets are forcing data-structure designers to consider seriously both parallel construction and compactness. To achieve those goals we need to design a parallel algorithm with good scalability and with low…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for computing ground state energies of molecular systems. We implement VQE to calculate the potential energy surface of the hydrogen molecule (H$_2$) across…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…
Nested parallelism exists in scientific codes that are searching multi-dimensional spaces. However, implementations of nested parallelism often have overhead and load balance issues. The Orbital Analysis code we present exhibits a sparse…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…