Related papers: Higher-order multi-scale method for high-accuracy …
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential.…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena.…
Power and efficiency of heat engines are two conflicting objectives, and a tight efficiency bound is expected to give insights on the fundamental properties of the power-efficiency tradeoff. Here we derive an upper bound on the efficiency…
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coefficients. A generalized Cordes condition is imposed to…
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…
Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
Complex soft matter systems can be efficiently studied with the help of adaptive resolution simulation methods, concurrently employing two levels of resolution in different regions of the simulation domain. The non-matching properties of…
The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
We establish higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems accompanied with rapidly oscillating initial data. Such result is new even for linear problems. Here we construct…
The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…