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The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions and computing them by fast Fourier transform (FFT), we reduce the computational complexity of PD…
Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling…
Peridynamics is a non-local continuum mechanics theory that offers unique advantages for modeling problems involving discontinuities and complex deformations. Within the peridynamic framework, various formulations exist, among which the…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods…
Ordinary state-based peridynamic (OSB-PD) models have an unparalleled capability to simulate crack propagation phenomena in solids with arbitrary Poisson's ratio. However, their non-locality also leads to prohibitively high computational…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
With the continuous growth of processing power for scientific computing, first principles Born-Oppenheimer molecular dynamics (MD) simulations are becoming increasingly popular for the study of a wide range of problems in materials science,…
The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods…
Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict…
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
In this work, we present a high-fidelity and efficient point-particle direct numerical simulation framework based on a multi-block overset curvilinear grid system, enabling large-scale Lagrangian particle tracking in complex geometries with…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous…