Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

2019 ◽  
Author(s):  
Houman Owhadi ◽  
Clint Scovel
Keyword(s):  
Numerical Homogenization ◽  
Fast Solvers

scholarly journals Numerical Homogenization of Multi-Layered Corrugated Cardboard with Creasing or Perforation

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3786
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska ◽  
Damian Mrówczyński
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Torsional Stiffness ◽  
Numerical Homogenization ◽  
Corrugated Board ◽  
3D Geometry ◽  
Corrugated Cardboard ◽  
Numerical Tools ◽  
Packaging Industry ◽  
Theoretical Considerations

The corrugated board packaging industry is increasingly using advanced numerical tools to design and estimate the load capacity of its products. This is why numerical analyses are becoming a common standard in this branch of manufacturing. Such trends cause either the use of advanced computational models that take into account the full 3D geometry of the flat and wavy layers of corrugated board, or the use of homogenization techniques to simplify the numerical model. The article presents theoretical considerations that extend the numerical homogenization technique already presented in our previous work. The proposed here homogenization procedure also takes into account the creasing and/or perforation of corrugated board (i.e., processes that undoubtedly weaken the stiffness and strength of the corrugated board locally). However, it is not always easy to estimate how exactly these processes affect the bending or torsional stiffness. What is known for sure is that the degradation of stiffness depends, among other things, on the type of cut, its shape, the depth of creasing as well as their position or direction in relation to the corrugation direction. The method proposed here can be successfully applied to model smeared degradation in a finite element or to define degraded interface stiffnesses on a crease line or a perforation line.

scholarly journals Estimating effective conductivity of unidirectional transversely isotropic composites

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Trung Kien ◽  
Nguyen Van Luat ◽  
Pham Duc Chinh
Keyword(s):  
Effective Conductivity ◽  
Fourier Method ◽  
Transversely Isotropic ◽  
Transverse Plane ◽  
Numerical Homogenization ◽  
Unidirectional Composites ◽  
Periodic Composites ◽  
Point Correlation ◽  
Correlation Parameters

Three-point correlation bounds are constructed on effective conductivity of unidirectional composites, which are isotropic in the transverse plane. The bounds contain, in addition to the properties and volume proportions of the component materials, three-point correlation parameters describing the micro-geometry of a composite, and are tighter those obtained in [1]. The bounds, applied to some disordered and periodic composites, keep inside the numerical homogenization results obtained by Fast Fourier method.

scholarly journals A comparison of the performance of depth-integrated ice-dynamics solvers

2021 ◽  
Author(s):  
Alexander Robinson ◽  
Daniel Goldberg ◽  
William H. Lipscomb
Keyword(s):  
Numerical Stability ◽  
Ice Sheet ◽  
Model Performance ◽  
Greenland Ice Sheet ◽  
Grid Resolution ◽  
Ice Dynamics ◽  
Fast Solvers ◽  
Ice Flow ◽  
Hybrid Solver ◽  
Constant Viscosity

Abstract. In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

Fast solvers for discrete systems

2015 ◽  
pp. 322-355
Author(s):  
Zhongying Chen ◽  
Charles A. Micchelli ◽  
Yuesheng Xu
Keyword(s):  
Discrete Systems ◽  
Fast Solvers

PAM-OPT™/PAM-SOLID™: Optimization of Transport Vehicle Crash and Safety Design and Forming Processes

1998 ◽  
Author(s):  
E. Haug ◽  
P. Guyon
Keyword(s):  
Sheet Metal Forming ◽  
Process Simulation ◽  
Metal Forming ◽  
Paper Briefly ◽  
Fast Solvers ◽  
Vehicle Crash ◽  
Safety Design ◽  
Transport Vehicle ◽  
Flow Charts ◽  
Vehicle Crashworthiness

Abstract Dynamic simulation solver codes are now extensively used by industry for the design verification of vehicle crashworthiness and for the process simulation of sheet metal forming. The logical next step is to use these by now proven codes for the optimization of the vehicle crash design and of metal forming processes. A step towards this goal has been taken by PSI, and an optimization code, PAM-OPT™, has been written for calling dynamic FE codes of the PAM-SOLID™ family in design and process optimization loops. The code interacts with the user via input, signalling and output files and it calls an interface that interacts with the FE solvers. The paper briefly outlines the properties and various flow charts of the optimizer, depending on single or multiple solvers used in the loop, single or parallel calls and fast solvers. Then the paper reports various applications of PAM-OPT™ in conjunction with the PAM-SFE™, PAM-CRASH™, PAM-SAFE™ and PAM-STAMP™ solvers. An outlook on how to replace the user-written interface with a general keyword-driven interface concludes the paper.

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