Related papers: Parallel-in-time high-order multiderivative IMEX s…
A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the problem is represented in two steps. The first preliminary…
Time integration of ODEs or time-dependent PDEs with required resolution of the fastest time scales of the system, can be very costly if the system exhibits multiple time scales of different magnitudes. If the different time scales are…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
In this paper, we propose a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, which dynamically detects regions of equilibrium and non-equilibrium. Our implementation automatically switches between Euler…
In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…
In this paper we propose a new parallel algorithm for solving global optimization (GO) multidimensional problems. The method unifies two powerful approaches for accelerating the search: parallel computations and local tuning on the behavior…
In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
This paper investigates co-scheduling algorithms for processing a set of parallel applications. Instead of executing each application one by one, using a maximum degree of parallelism for each of them, we aim at scheduling several…
We present a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a multi-implicit spectral deferred correction (MISDC)…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
In this paper, we propose a new parallel ordering method to vectorize and parallelize the sparse triangular solver, which is called hierarchical block multi-color ordering. In this method, the parallel forward and backward substitutions can…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
We analyze composition methods with complex coefficients exhibiting the so-called ``symmetry-conjugate'' pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative properties when…