The advent of advanced processing andmanufacturing techniques has led to newmaterial classes with complexmicrostructures across scales from nanometers to meters. In this paper, a data-driven computational framework fo...
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ISBN:
(纸本)9783030151195;9783030151188
The advent of advanced processing andmanufacturing techniques has led to newmaterial classes with complexmicrostructures across scales from nanometers to meters. In this paper, a data-driven computational framework for the analysis of these complex material systems is presented. A mechanistic concurrent multiscale method called Self-consistent Clustering Analysis (SCA) is developed for general inelastic heterogeneous material systems. The efficiency of SCA is achieved via data compression algorithms which group local microstructures into clusters during the training stage, thereby reducing required computational expense. Its accuracy is guaranteed by introducing a self-consistent method for solving the Lippmann-Schwinger integral equation in the prediction stage. The proposed framework is illustrated for a composite cutting process where fracture can be analyzed simultaneously at the microstructure and part scales.
In this paper we are concerned with the efficient approximation of the Schrodinger eigenproblem using an orbital-enriched flat-top partition of unity method on general triclinic cells. To this end, we generalize the a...
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ISBN:
(纸本)9783030151195;9783030151188
In this paper we are concerned with the efficient approximation of the Schrodinger eigenproblem using an orbital-enriched flat-top partition of unity method on general triclinic cells. To this end, we generalize the approach presented in Albrecht et al. (Comput. Meth. Appl. Mech. Eng. 342:224-239, 2018) via a simple yet effective transformation approach and discuss its realization in the PUMA software framework. The presented results clearly show that the proposed scheme attains all convergence and stability properties presented in Albrecht et al.
Fluid Structure Interaction ( FSI) and meshfree numerical methods are a perfect couple. One often repeated strong argument is the almost natural coupling of meshfree methods in a Lagrangian/ALE formulation with moving...
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ISBN:
(纸本)9783030151195;9783030151188
Fluid Structure Interaction ( FSI) and meshfree numerical methods are a perfect couple. One often repeated strong argument is the almost natural coupling of meshfree methods in a Lagrangian/ALE formulation with moving, flexible structures. Since 1996, Fraunhofer ITWM has been developing a Generalized Finite Difference Method (GFDM), a purelymeshfree solver for fluid and continuum mechanics. In the industrial context, this method is also referred to as Finite Pointset Method (FPM). Currently, it is further developed to an integrated tool called MESHFREE which combines the advantages of GFDM/FPM as well as SAMG, a fast solver for large sparse linear systems developed by Fraunhofer SCAI. This synergy drastically increases the applicability of themethod since SAMG provides a robust and scalable linear solver for a wide class of problems. In this contribution, we classify fundamental FSI aspects in GFDM/FPM: classical pressure-velocity coupling and alternative velocity-pressure coupling. Each category will be illustrated by industrially relevant examples, with special focus on Pelton turbine applications and flow in flexible tubes.
In uncertainty quantification, an unknown quantity has to be reconstructed which depends typically on the solution of a partial differential equation. This partial differential equation itself may depend on parameters...
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ISBN:
(纸本)9783030151195;9783030151188
In uncertainty quantification, an unknown quantity has to be reconstructed which depends typically on the solution of a partial differential equation. This partial differential equation itself may depend on parameters, some of them may be deterministic and some are random. To approximate the unknown quantity one therefore has to solve the partial differential equation (usually numerically) for several instances of the parameters and then reconstruct the quantity from these simulations. As the number of parameters may be large, this becomes a highdimensional reconstruction problem. We will address the topic of reconstructing such unknown quantities using kernel-based reconstruction methods on sparse grids. First, we will introduce into the topic, then explain the reconstruction process and finally provide new error estimates.
In this paper we present the global-local enrichment approach in a general partition of unity method. Moreover, we propose an automatic scheme of computing an optimal parameter in Robin boundary conditions for the loc...
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ISBN:
(纸本)9783030151195;9783030151188
In this paper we present the global-local enrichment approach in a general partition of unity method. Moreover, we propose an automatic scheme of computing an optimal parameter in Robin boundary conditions for the local problem. We present results of two dimensional fracture mechanics problems to demonstrate the properties and performance of the resulting method.
In this article we present a Radial Basis Function (RBF)-Finite Difference (FD) level set based method for the numerical solution of partial differential equations (PDEs) of the reaction-diffusion-convection type on a...
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ISBN:
(纸本)9783030151195;9783030151188
In this article we present a Radial Basis Function (RBF)-Finite Difference (FD) level set based method for the numerical solution of partial differential equations (PDEs) of the reaction-diffusion-convection type on an evolving-in-time hypersurface Gamma(t). In a series of numerical experiments we study the accuracy and robustness of the proposed scheme and demonstrate that the method is applicable to practical models.
The Finite Pointset Method (FPM) is a meshfree method for simulations in the field of fluid dynamics and continuum mechanics (Tiwari and Kuhnert, Finite pointset method based on the projection method for simulations o...
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ISBN:
(纸本)9783030151195;9783030151188
The Finite Pointset Method (FPM) is a meshfree method for simulations in the field of fluid dynamics and continuum mechanics (Tiwari and Kuhnert, Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations. Springer, Berlin, 2003). The key idea in FPM is to discretize the necessary differential operators by using stencils generated by a least squares approach on a pointcloud that is moving in every time step. Applying Algebraic Multigrid Methods (AMG) to the linear systems arising in FPM comes with various challenges, see our previous work Metsch et al. (Comput Vis Sci, reviewed) and Nick et al. (Linear solvers for the finite pointset method. In: Schafer, M., Behr, M., Mehl, M., Wohlmuth, B. (eds.) Recent advances in computationalengineering. Springer, Cham, 2018). In Nick et al. (Linear solvers for the finite pointset method. In: Schafer, M., Behr, M., Mehl, M., Wohlmuth, B. (eds.) Recent advances in computationalengineering. Springer, Cham, 2018) we limited ourselves to essentially irreducible matrices, saying that if a matrix arising from FPM is not essentially irreducible, we can employ a parallel algorithm in order to detect those subsystems that are essentially irreducible. This paper introduces the algorithm that we use in order to detect independent parts of the FPM pointcloud, which we call components. The algorithm that we propose has a theoretical complexity of O(vertical bar V vertical bar) in the average case, where vertical bar V vertical bar is the number of points in the pointcloud. Our experiments with a real world model however show that in practice the complexity is much better. The experiments also show that in order to guarantee a stable convergence of the arising linear systems, detecting components is essential, as singular components can occur in certain situations.
This paper presents an up-to-date Lagrangian particle method for the analysis of a coupled thermo-mechanical problem in the friction drilling simulation. The method is obtained by a modification of variational equatio...
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ISBN:
(纸本)9783030151195;9783030151188
This paper presents an up-to-date Lagrangian particle method for the analysis of a coupled thermo-mechanical problem in the friction drilling simulation. The method is obtained by a modification of variational equations using the penalized approach to avoid onerous stability problems in conventional Lagrangian particle methods and to obtain semi-discrete equations that are amenable to temporal and spatial integration using the staggered explicit time marching scheme. To deal with the critical numerical limitation associated with large deformation and material separation at the bushing forming stage, the method is furnished with an adaptive anisotropic Lagrangian kernel and a bond-based failure criterion. Representative simulation of a thermal-mechanical coupled friction drilling process is studied, and results are comparedwith the experimental data to examine the validity of this study.
The classical form of the Method of Fundamental Solutions is applied. Instead of using a single set of subtly located external sources, a special strategy of defining several sets of external source points is introduc...
ISBN:
(纸本)9783030151195;9783030151188
The classical form of the Method of Fundamental Solutions is applied. Instead of using a single set of subtly located external sources, a special strategy of defining several sets of external source points is introduced. The sets of sources are defined by the quadtree/octtree subdivision technique controlled by the boundary collocation points in a completely automatic way, resulting in a point set, the density of the spatial distribution of which decreases quickly far from the boundary. The 'far' sources are interpreted to form a 'coarse grid', while the densely distributed 'near-boundary' sources are considered a 'fine grid' (despite they need not to have any grid structure). Based on this classification, a multi- level technique is built up, where the smoothing procedure is defined by performing some familiar iterative technique e.g. the (conjugate) gradient method. The approximate solutions are calculated by enforcing the boundary conditions in the sense of least squares. The resulting multi-level method is robust and significantly reduces the computational cost. No weakly or strongly singular integrals have to be evaluated. Moreover, the problem of severely ill-conditioned matrices is completely avoided.
This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEM(gl)) and the Stable GFEM(gl). The preconditioners take advantag...
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ISBN:
(纸本)9783030151195;9783030151188
This paper focuses on preconditioners for the conjugate gradient method and their applications to the Generalized FEM with global-local enrichments (GFEM(gl)) and the Stable GFEM(gl). The preconditioners take advantage of the hierarchical struture of the matrices in these methods and the fact that most of the matrix does not change when simulating for example, the evolution of interfaces and fractures. The performance of the conjugate gradient method with the proposed preconditioner is investigated. A 3-D fracture problem is adopted for the numerical experiments.
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