Higher-continuity s-version of finite element method with B-spline functions

This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions, it has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure. However, it has disadvantages such as accuracy of numerical integration and matrix singularity. Although several additional techniques have been proposed to mitigate these limitations, they are computationally expensive or ad-hoc, and detract from its strengths. To solve these issues, we propose a novel strategy called B-spline based SFEM. To improve the accuracy of numerical integration, we employed cubic B-spline basis functions with $C^2$-continuity across element boundaries as the global basis functions. To avoid matrix singularity, we applied different basis functions to different meshes. Specifically, we employed the Lagrange basis functions as local basis functions. The numerical results indicate that using the proposed method, numerical integration can be calculated with sufficient accuracy without any additional techniques used in conventional SFEM. Furthermore, the proposed method avoids matrix singularity and is superior to conventional methods in terms of convergence for solving linear equations. Therefore, the proposed method has the potential to reduce computation time while maintaining a comparable accuracy to conventional SFEM.Comment: 40 pages, 15 figures and 2 table

2D Slice-driven Physics-based 3D Motion Estimation Framework for Pancreatic Radiotherapy

Pancreatic diseases are difficult to treat with high doses of radiation, as they often present both periodic and aperiodic deformations. Nevertheless, we expect that these difficulties can be overcome, and treatment results may be improved with the practical use of a device that can capture 2D slices of organs during irradiation. However, since only a few 2D slices can be taken, the 3D motion needs to be estimated from partially observed information. In this study, we propose a physics-based framework for estimating the 3D motion of organs, regardless of periodicity, from motion information obtained by 2D slices in one or more directions and a regression model that estimates the accuracy of the proposed framework to select the optimal slice. Using information obtained by slice-to-slice registration and setting the surrounding organs as boundaries, the framework drives the physical models for estimating 3D motion. The R2 score of the proposed regression model was greater than 0.9, and the RMSE was 0.357 mm. The mean errors were 5.11 $\pm$ 1.09 mm using an axial slice and 2.13 $\pm$ 0.598 mm using concurrent axial, sagittal, and coronal slices. Our results suggest that the proposed framework is comparable to volume-to-volume registration, and is feasible

Compatible interface wave–structure interaction model for combining mesh-free particle and finite element methods

Abstract This study presents a novel wave–structure interaction model, which is a compatible interface wave–structure interaction model that is based on mesh-free particle methods for free-surface flow analysis; the FEM for structural analysis. We adopt the explicitly represented polygon (ERP) wall boundary model, which is a polygon wall boundary model for mesh-free particle methods, to express the fluid–structure interfaces. The fluid–structure interfaces in the proposed model are geometrically compatible because the ERP model has advantages in dealing with complex-shaped and moving boundaries and it enables the direct use of surface meshes and shape functions given by finite element models of structures. This allows the automatic generation of polygons for free-surface flow analysis from finite elements, and therefore, it greatly increases the flexibility of the analysis. Based on the compatible interface between the polygons and finite elements, we propose a strong coupling algorithm based on an iterative partitioned scheme that defines the interacting models between the fluid and the structure. We model the force exerted by fluid particles on structures such that the kinetic boundary condition on the fluid–structure interface is satisfied. We perform the verification and validation tests of the proposed model by solving two benchmark problems

Visualization using implicit function represantation using Paraview and Unreal Engine 5 for dam break problem

This media shows an example of Paraview and Unreal Engine 5-based visualization of the dam break problem. The dam break problem was analyzed using the smoothed particle hydrodynamics method. The simulation results were transformed into an implicit function representation by particle number density and visualized by Paraview and Unreal Engine 5.</p