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We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
This paper developes a data-driven magnetostatic finite-element (FE) solver which directly exploits measured material data instead of a material curve constructed from it. The distances between the field solution and the measurement points…
A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…
The spatial properties of the solar magnetic field are crucial to decoding the physical processes in the solar interior and their interplanetary effects. However, observations from older instruments, such as the Michelson Doppler Imager…
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Phase-field models of liquid metal dealloying (LMD) can resolve rich microstructural dynamics but become intractable for large domains or long time horizons. We present a conditionally parameterized, fully convolutional U-Net surrogate that…
The transmission of light through an ensemble of two-level emitters in a one-dimensional geometry is commonly described by one of two emblematic models of quantum electrodynamics (QED): the driven-dissipative Dicke model or the…
Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many…
In this study, the open-source finite-difference time-domain (FDTD) solvers gprMax, Elecode and MEEP are investigated for their suitability to compute lightning electromagnetic field propagation. Several simulations are performed to…
In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the…
A three-step model for calculating the magnetic field generated by coils inside cuboid-shaped shields like magnetically shielded rooms (MSRs) is presented. The shield is modelled as two parallel plates of infinite width and one tube of…
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…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the…
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
The Earth Mover's Distance (EMD) computes the optimal cost of transforming one distribution into another, given a known transport metric between them. In deep learning, the EMD loss allows us to embed information during training about the…