Related papers: Efficient and realistic 3-D Boundary Element simul…
Emulation has been successfully applied across a wide variety of scientific disciplines for efficiently analysing computationally intensive models. We develop known boundary emulation strategies which utilise the fact that, for many…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
For low dimension systems admitting a moment equation representation (MER), the development of an effective eigenenergy bounding theory applicable to all discrete states had remained elusive, until now. Whereas Handy et al (1988 Phys. Rev.…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial…
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…
Electromagnetic methods have become one of the most widely used techniques in geological exploration. With the remarkable success of deep learning, applying such techniques to EM methods has emerged as a promising research direction to…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…
In the context of high performance finite element analysis, the cost of iteratively modifying a computational domain via re-meshing and restarting the analysis becomes time prohibitive as the size of simulations increases. In this paper, we…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and…
A highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton-Miller boundary integral…
The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…
The frequency-domain fast boundary element method (BEM) combined with the exponential window technique leads to an efficient yet simple method for elastodynamic analysis. In this paper, the efficiency of this method is further enhanced by…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…