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A formulation of the asymptotically exact first-order shear deformation theory for linear-elastic homogeneous plates in the rescaled coordinates and rotation angles is considered. This allows the development of its asymptotically accurate…
Exciton diffusion plays a vital role in the function of many organic semiconducting opto-electronic devices, where an accurate description requires precise control of heterojunctions. This poses a challenging problem because the…
In this work, we extend the meshfree generalized multiscale exponential integration framework introduced in Nikiforov et al. (2025) to the simulation of three-dimensional advection--diffusion problems in heterogeneous and high-contrast…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
Large-scale multi-objective optimization poses challenges to existing evolutionary algorithms in maintaining the performances of convergence and diversity because of high dimensional decision variables. Inspired by the motion of particles…
Diffusion models have recently emerged as powerful generative models in medical imaging. However, it remains a major challenge to combine these data-driven models with domain knowledge to guide brain imaging problems. In neuroimaging,…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
Conditional medical image generation plays an important role in many clinically relevant imaging tasks. However, existing methods still face a fundamental challenge in balancing inference efficiency, patient-specific fidelity, and…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…
A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(\Omega,\mathbb{R}^{d\times d}_{sym})$…
Recent developments in high peak-power table-top laser systems reaching highly relativistic light intensities have led to significant advances in laser-driven particle acceleration schemes (mainly the laser wakefield acceleration, LWFA)…
We consider special upwinding Petrov-Galerkin discretizations for convection-diffusion problems. For the one dimensional case with a standard continuous linear element as the trial space and a special exponential bubble test space, we prove…
We are interested in the high-order approximation of anisotropic, potential-driven advection-diffusion models on general polytopal partitions. We study two hybrid schemes, both built upon the Hybrid High-Order technology. The first one…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that…
We construct and analyze approximation rates of deep operator networks (ONets) between infinite-dimensional spaces that emulate with an exponential rate of convergence the coefficient-to-solution map of elliptic second-order partial…