An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

We propose an explicit GPU-based solver within the material point method (MPM) framework using graphics processing units (GPUs) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e. granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and non-local computational aspects (i.e. the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report (i) a maximum 200-fold performance gain between a CPU- and a single-GPU-based implementation, provided that (ii) the hardware limit (i.e. the peak memory bandwidth) of the device is reached. Furthermore, our multi-GPU implementation can resolve models with nearly a billion material points. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.

Numerical Investigation of Shallow Liquid Sloshing in a Baffled Tank and the Associated Damping Effect by BM-MPS Method

Understanding the damping mechanism of baffles is helpful to make more reasonable use of them in suppressing liquid sloshing. In this study, the damping effect and mechanism of vertical baffles in shallow liquid sloshing under a rotational excitation are investigated by an improved particle method. By incorporation of a background mesh scheme and a modified pressure gradient model, the accuracy of impact pressure during sloshing is significantly enhanced. Combined with the advantages of the particle method, the present numerical method is a wonderful tool for the investigation of liquid sloshing issues. Through the analysis of impact pressure, the influences of baffle height and baffle position on the damping mechanism are discussed. The results show that the damping effect of vertical baffles increases with the increase of the elevation of baffle top and decreases with the increase of the elevation of the baffle bottom. Moreover, the resonance characteristics of sloshing are altered when static water is divided into two parts by the vertical baffle. The dominant damping mechanism of vertical baffles depends on the configurations.

Immersed boundary-conformal isogeometric method for linear elliptic problems

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage the geometric flexibility of the immersed boundary method with the advantages of a conformal discretization, such as intuitive control of mesh resolution around the boundary, higher accuracy per degree of freedom, automatic satisfaction of interface kinematic conditions, and the ability to strongly impose Dirichlet boundary conditions. In the proposed method, starting with a boundary representation of a geometric model, we extrude it to obtain a corresponding conformal layer. Next, a given background B-spline mesh is cut with the conformal layer, leading to two disconnected regions: an exterior region and an interior region. Depending on the problem of interest, one of the two regions is selected to be coupled with the conformal layer through Nitsche’s method. Such a construction involves Boolean operations such as difference and union, which therefore require proper stabilization to deal with arbitrarily cut elements. In this regard, we follow our precedent work called the minimal stabilization method (Antolin et al in SIAM J Sci Comput 43(1):A330–A354, 2021). In the end, we solve several 2D benchmark problems to demonstrate improved accuracy and expected convergence with IBCM. Two applications that involve complex geometries are also studied to show the potential of IBCM, including a spanner model and a fiber-reinforced composite model. Moreover, we demonstrate the effectiveness of IBCM in an application that exhibits boundary-layer phenomena.

An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

We propose an explicit GPU-based solver within the material point method (MPM) framework on a single graphics pro- cessing unit (GPU) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e., granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and nonlocal computational aspects (i.e., the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report i) a maximum performance gain of x200 between a CPU- and GPU-based implementation, provided that ii) the hardware limit (i.e., the peak memory bandwidth) of the device is reached. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.

Automatic sizing functions for unstructured mesh generation revisited

PurposeSizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.Design/methodology/approachA practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.FindingsThe local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.Originality/valueTheoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

In many geomechanics applications, material boundaries are subjected to large displacements and deformation. Under these circumstances, the application of boundary conditions using particle methods, such as the material point method (MPM), becomes a challenging task since material boundaries do not coincide with the background mesh. This paper presents a formulation of penalty augmentation to impose nonhomogeneous, nonconforming Dirichlet boundary conditions in implicit MPM. The penalty augmentation is implemented utilizing boundary particles, which can move either according to or independently from the material deformation. Furthermore, releasing contact boundary condition, as well as the capability to accommodate slip boundaries, is introduced in the current work. The accuracy of the proposed method is assessed in both 2D and 3D cases, by convergence analysis reaching the analytical solution and by comparing the results of nonconforming and classical grid-conforming simulations.

A cut finite element method for a model of pressure in fractured media

We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion. Starting from a common background bulk mesh, that covers the domain, finite element spaces are constructed for the interface and bulk subdomains leading to efficient computations of the coupling terms. The crack pressure field also uses the bulk mesh for its representation. The interface conditions are a generalized form of conditions of Robin type previously considered in the literature which allows the modeling of a range of flow regimes across the fracture. The method is robust in the following way: (1) Stability of the formulation in the full range of parameter choices; and (2) Not sensitive to the location of the interface in the background mesh. We derive an optimal order a priori error estimate and present illustrating numerical examples.

Study on the Manifold Cover Lagrangian Integral Point Method Based on Barycentric Interpolation

To achieve numerical simulation of large deformation evolution processes in underground engineering, the barycentric interpolation test function is established in this paper based on the manifold cover idea. A large-deformation numerical simulation method is proposed by the double discrete method with the fixed Euler background mesh and moving material points, with discontinuous damage processes implemented by continuous simulation. The material particles are also the integration points. This method is called the manifold cover Lagrangian integral point method based on barycentric interpolation. The method uses the Euler mesh as the background integral mesh and describes the deformation behavior of macroscopic objects through the motion of particles between meshes. Therefore, this method can avoid the problem of computation termination caused by the distortion of the mesh in the calculation process. In addition, this method can keep material particles moving without limits in the set region, which makes it suitable for simulating large deformation and collapse problems in geotechnical engineering. Taking a typical slope as an example, the results of a slope slip surface obtained using the manifold cover Lagrangian integral point method based on barycentric interpolation proposed in this paper were basically consistent with the theoretical analytical method. Hence, the correctness of the method was verified. The method was then applied for simulating the collapse process of the side slope, thereby confirming the feasibility of the method for computing large deformations.