General finite-volume framework for saddle-point problems of various physics

This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

A novel surface-integral-equation formulation for efficient and accurate electromagnetic analyses of near-zero-index structures

We consider accurate and iteratively efficient solutions of electromagnetic problems involving homogenized near-zero-index (NZI) bodies using surface-integral-equation formulations in frequency domain. NZI structures can be practically useful in a plethora of optical applications, as they possess near-zero permittivity and/or permeability values that cannot be found in nature. Hence, numerical simulations are of utmost importance for rigorous design and analyses of NZI structures. Unfortunately, small values of electromagnetic parameters bring computational challenges in numerical solutions of homogeneous models. Conventional formulations available in the literature encounter stability issues that make them inaccurate and/or inefficient as permittivity and/or permeability approach zero. We propose a novel formulation that involves a well-balanced combination of operators and that can provide both accurate and efficient solutions of all NZI cases. Numerical results are presented to demonstrate the superior properties of the developed formulation in comparison to the conventional ones.

Surface integral and focusing

Surface integral and focusing

Surface integral and focusing

Surface integral and focusing

Surface integral and focusing

Surface holographic integral and focusing

Carbene Ligand-Doped Fe2O3 Composite for Rapid Removal of Multiple Dyes under Sunlight

Contaminated water due to industrial organic dyes presents a significant challenge to sustainability. As a material of green energy, photocatalysts offer an effective and environmentally friendly way to deal with organic dyes for water treatment. A series of simple and highly efficient iron photocatalysts with carbene ligands were developed, which, under the illumination of sunlight, can rapidly degrade multiple organic dyes in water at room temperature, including rhodamine B (RhB), indigo carmine (IC), methyl blue (MB), and congo red (CR). The field-only surface integral method was carried out to determine the absorption spectrum of photocatalyst particles. Under the optimized experimental conditions which were selected by the orthogonal experiments for four dyes, 0.5a@Fe2O3 and 2c@Fe2O3 demonstrated good stability and photocatalytic activity. These two composite materials not only have the ability to remove 98.0% of the degradation in 10 s, but also maintain high reactivity after a few cycles of repeated use.