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Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…
In this paper, a high order implicit Method of Line Transpose (MOL$^T$ ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the…
In this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
Meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-Implicit (MPS) method, are widely used to simulate complex free-surface and multiphase flows. A key challenge in these methods is the…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
In this technical report, we investigate efficient representations of articulated objects (e.g. human bodies), which is an important problem in computer vision and graphics. To deform articulated geometry, existing approaches represent…
Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…
This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…
This paper presents a virtual boundary integral neural network (VBINN) for exterior acoustic problems in three dimensions. The method introduces a virtual boundary inside the scatterer or vibrating body and represents the associated source…
We present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep…
This work studies shape filtering techniques, namely the convolution-based (explicit) and the PDE-based (implicit), and introduces an implicit bulk-surface filtering method to control the boundary smoothness and preserve the internal mesh…
This paper presents an immersed boundary (IB) method for fluid--structure--acoustics interactions involving large deformations and complex geometries. In this method, the fluid dynamics is solved by a finite difference method where the…
Accurate and efficient physical simulations are essential in science and engineering, yet traditional numerical solvers face significant challenges in computational cost when handling simulations across dynamic scenarios involving complex…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…