Related papers: Learning Mesh Motion Techniques with Application t…
For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping…
The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…
Our paper proposes an innovative approach for modeling Fluid-Structure Interaction (FSI). Our method combines both traditional monolithic and partitioned approaches, creating a hybrid solution that facilitates FSI. At each time iteration,…
A comparative study on mesh-based and mesh-less Computational Fluid Dynamics (CFD) approaches coupled with the Discrete Element Method (DEM) is presented. As the mesh-based CFD approach a Finite Volume Method (FVM) is used. A Smoothed…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
A unifying moving mesh method is developed for general $m$-dimensional geometric objects in $d$-dimensions ($d \ge 1$ and $1\le m \le d$) including curves, surfaces, and domains. The method is based on mesh equidistribution and alignment…
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
Learning solution operators for partial differential equations (PDEs) has become a foundational task in scientific machine learning. However, existing neural operator methods require abundant training data for each specific PDE and lack the…
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170…
A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the…
In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure…
In this work, we present a novel method for the mesh update in flow problems with moving boundaries, the phantom domain deformation mesh update method (PD-DMUM). The PD-DMUM is designed to avoid remeshing; even in the event of large,…
Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…
Aquatic locomotion is a classic fluid-structure interaction (FSI) problem of interest to biologists and engineers. Solving the fully coupled FSI equations for incompressible Navier-Stokes and finite elasticity is computationally expensive.…
Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh method is provided for a moving boundary problem related to…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
Muscle forces and joint kinematics estimated with musculoskeletal (MSK) modeling techniques offer useful metrics describing movement quality. Model-based computational MSK models can interpret the dynamic interaction between the neural…