Search results for "boundary"
showing 10 items of 1626 documents
A 3D multi-physics boundary element computational framework for polycrystalline materials micro-mechanics
2021
A recently developed novel three-dimensional (3D) computational framework for the analysis of polycrystalline materials at the grain scale is described in this lecture. The framework is based on the employment of: i) 3D Laguerre-Voronoi tessellations for the representation of the micro-morphology of polycrystalline materials; ii) boundary integral equations for the representation of the mechanics of the individual grains; iii) suitable cohesive traction-separation laws for the representation of the multi-physics behavior of the interfaces (either inter-granular or trans-granular) within the aggregate, which are the seat of damage initiation and evolution processes, up to complete decohesion…
A mixed finite element method for the heat flow problem
1981
A semidiscrete finite element scheme for the approximation of the spatial temperature change field is presented. The method yields a better order of convergence than the conventional use of linear elements.
A Meshfree Solver for the MEG Forward Problem
2015
Noninvasive estimation of brain activity via magnetoencephalography (MEG) involves an inverse problem whose solution requires an accurate and fast forward solver. To this end, we propose the Method of Fundamental Solutions (MFS) as a meshfree alternative to the Boundary Element Method (BEM). The solution of the MEG forward problem is obtained, via the Method of Particular Solutions (MPS), by numerically solving a boundary value problem for the electric scalar potential, derived from the quasi-stationary approximation of Maxwell’s equations. The magnetic field is then computed by the Biot-Savart law. Numerical experiments have been carried out in a realistic single-shell head geometry. The p…
High Precision Conservative Surface Mesh Generation for Swept Volumes
2015
We present a novel, efficient, and flexible scheme to generate a high-quality mesh that approximates the outer boundary of a swept volume. Our approach comes with two guarantees. First, the approximation is conservative, i.e., the swept volume is enclosed by the generated mesh. Second, the one-sided Hausdorff distance of the generated mesh to the swept volume is upper bounded by a user defined tolerance. Exploiting this tolerance the algorithm generates a mesh that is adapted to the local complexity of the swept volume boundary, keeping the overall output complexity remarkably low. The algorithm is two-phased: the actual sweep and the mesh generation. In the sweeping phase, we introduce a g…
DORA algorithm for network flow models with improved stability and convergence properties
2001
A new methodology for the solution of shallow water equations is applied for the computation of the unsteady-state flow in an urban drainage network. The inertial terms are neglected in the momentum equations and the solution is decoupled into one kinematic and one diffusive component. After a short presentation of the DORA (Double ORder Approximation) methodology in the case of a single open channel, the new methodology is applied to the case of a sewer network. The transition from partial to full section and vice versa is treated without the help of the Preissmann approximation. The algorithm also allows the computation of the diffusive component in the case of vertical topographic discon…
A multi-domain approach for smoothed particle hydrodynamics simulations of highly complex flows
2018
Abstract An efficient and accurate method is proposed to solve the incompressible flow momentum and continuity equations in computational domains partitioned into subdomains in the framework of the smoothed particle hydrodynamics method. The procedure does not require any overlap of the subdomains, which would result in the increase of the computational effort. Perfectly matching solutions are obtained at the surfaces separating neighboring blocks. The block interfaces can be both planar and curved surfaces allowing to easily decompose even geometrically complex domains. The smoothing length of the kernel function is maintained constant in each subdomain, while changing between blocks where…
Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving
2020
AbstractPhysical models for equation solving typically lack feedback regarding their appropriate use. Such feedback is possible in virtual environments and could be implemented in hybrid models. Based on an epistemological analysis, this article presents a touch gesture as a way for users to signal they want to divide both sides of an equation and a design for feedback on the use of this so-called ‘division gesture’. The design is investigated by contrasting a case study, in which students used an app with the division gesture, with a preparatory study where students had to perform corresponding actions on physical manipulatives. This investigation revealed insight into feedback functions, …
A hybrid virtual–boundary element formulation for heterogeneous materials
2021
Abstract In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary i…
Investigation of Finite-Size Effects in the Determination of Interfacial Tensions
2014
The interfacial tension between coexisting phases of a material is an important parameter in the description of many phenomena such as crystallization, and even today its accurate measurement remains difficult. We have studied logarithmic finite-size corrections in the determination of the interfacial tension with large scale Monte Carlo simulations, and have identified several novel contributions which not only depend on the ensemble, but also on the type of the applied boundary conditions. We present results for the Lennard-Jones system and the Ising model, as well as for hard spheres, which are particularly challenging. In the future, these findings will contribute to the understanding a…
Theoretical Foundations of the Monte Carlo Method and Its Applications in Statistical Physics
2002
In this chapter we first introduce the basic concepts of Monte Carlo sampling, give some details on how Monte Carlo programs need to be organized, and then proceed to the interpretation and analysis of Monte Carlo results.