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We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…
High-Q optical resonances in photonic microcavities are investigated numerically using a time-harmonic finite-element method.
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
We propose highly accurate finite-difference schemes for simulating wave propagation problems described by linear second-order hyperbolic equations. The schemes are based on the summation by parts (SBP) approach modified for applications…
In this paper, a direct finite element method is proposed for solving interface problems on unfitted meshes. This new method treats the two interface conditions as an $H^{\frac12}(\Gamma)\times H^{-\frac12}(\Gamma)$ pair for the mutual…
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous…
The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an…
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical…
We investigate nonlinear one- and two-dimensional photonic crystals by applying a finite element-iterative method.Numerical results show the essential influence of nonlinear elements embedded into a quarter-wave stack and the sharp photonic…
This study introduces a systematic and optimised methodology for designing Linear Variable Differential Transformer (LVDT) sensors and Voice Coil (VC) actuators, tailored for high-precision applications such as gravitational wave detectors…
This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…
We present a new parallel spectral element solver, FNPF-SEM, for simulating linear and fully nonlinear potential flow-based water waves and their interaction with offshore structures. The tool is designed as a general-purpose wave model for…
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…