Related papers: Assembly of multiscale linear PDE operators
The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a…
First-principles atomistic simulations are essential for understanding complex material phenomena but are fundamentally limited by their computational cost. While Machine Learning Interatomic Potentials (MLIPs) have drastically improved…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
In a recent paper, {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)}, we discussed two algorithms for deforming and contracting a simply connected discrete closed manifold into a discrete sphere.…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
We consider approximating solutions to parameterized linear systems of the form $A(\mu_1,\mu_2) x(\mu_1,\mu_2) = b$. Here the matrix $A(\mu_1,\mu_2) \in \mathbb{R}^{n \times n}$ is nonsingular, large, and sparse and depends nonlinearly on…
This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or…
We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the…
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear…
We consider the eigenvalue equation for the largest eigenvalue of certain kinds of non-compact linear operators given as the sum of a multiplication and a kernel operator. It is shown that, under moderate conditions, such operators can be…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
This paper addresses the problem of decentralized abstractions for multiple mobile manipulators with 2nd order dynamics. In particular, we propose decentralized controllers for the navigation of each agent among predefined regions of…
Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we discuss an extension to the…