Related papers: Random Batch Methods for Discretized PDEs on Graph…
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…
One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…
Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a…
We study the numerical approximation of a class of degenerate parabolic stochastic partial differential equations on non-compact metric graphs, which naturally arise in the asymptotic analysis of Hamiltonian flows under small noise…
We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces---generalized by the term hypergraphs. To this end, we consider PDEs on…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…