相关论文: HiPhom$\varepsilon$ -: HIgh order Projection-based…
Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from the non-convex nature of the optimization problem with multiple local optima, which usually requires a…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We design a Hybrid High-Order (HHO) scheme for the Poisson problem that is fully robust on polytopal meshes in the presence of small edges/faces. We state general assumptions on the stabilisation terms involved in the scheme, under which…
Hybrid High-Order methods for elliptic diffusion problems have been originally formulated for loads in the Lebesgue space $L^2(\Omega)$. In this paper we devise and analyze a variant thereof, which is defined for any load in the dual…
This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…
A multiscale asymptotic homogenization method for periodic microstructured materials in presence of thermoelasticity with periodic spatially dependent one relaxation time is introduced. The asymptotic expansions of the micro-displacement…
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…
Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…
In reservoir simulation, solution of the coupled systems of nonlinear algebraic equations that are associated with fully-implicit (backward Euler) discretization is challenging. Having a robust and efficient nonlinear solver is necessary in…
The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…
An improved numerical scheme is proposed for advection-dominated advection-diffusion problem. The scheme is based on Galerkin finite element method (FEM) with basis enriched with approximations to residual-free bubbles. The stabilisation…
As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp…
Recent diffusion and flow matching models have demonstrated strong capabilities in image generation and editing by progressively removing noise through iterative sampling. While this enables flexible inversion for semantic-preserving edits,…
In this paper we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows for a significant reduction in the variance for the…
In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications…
The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is…