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We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is…
This study evaluates numerical discretization methods for the Single Particle Model (SPM) used in electrochemical modeling. The methods include the Finite Difference Method (FDM), spectral methods, Pad\'e approximation, and parabolic…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…
In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as…
Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
In this paper, 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…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
While Dynamic Convolution (DY-Conv) has shown promising performance by enabling adaptive weight selection through multiple parallel weights combined with an attention mechanism, the frequency response of these weights tends to exhibit high…
Developing new methods for the accurate and efficient calculations of real-time quantum correlation functions is deemed one of the most challenging problems of modern condensed matter theory. Many popular methods, such as centroid molecular…
Computed tomography (CT) is widely used in scientific imaging systems such as synchrotron and laboratory-based nano-CT, but acquiring full-view sinograms requires high radiation dose and long scan times. Sparse-view CT reduces this burden…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
Convolutional neural networks (CNNs) have gained tremendous success in solving complex inverse problems. The aim of this work is to develop a novel CNN framework to reconstruct video sequence of dynamic live cells captured using a…
The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range…
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning…
Functional brain network (FBN) modeling often relies on local pairwise interactions, whose limitation in capturing high-order dependencies is theoretically analyzed in this paper. Meanwhile, the computational burden and heuristic nature of…
We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…