Combining set propagation with finite element methods for time integration in transient solid mechanics problems

Forets, Marcelo; Freire, Daniel; Zerpa, Jorge M. Pérez

doi:10.1016/j.compstruc.2021.106699

Cited by 5 publications

(2 citation statements)

References 51 publications

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“…We have recently applied LazySets to compute reachable states for linear wave propagation problems and heat transfer problems [14].…”

Section: Origin Of Lazysets and Current Applicationsmentioning

confidence: 99%

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

2021

JCON

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LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. LazySets provides methods to apply common set operations, convert between different set representations, and efficiently compute with sets in high dimensions using specialized algorithms based on the set types. LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. While the library was originally designed for reachability and formal verification, its scope goes beyond such topics. LazySets is an easy-to-use, general-purpose and scalable library for computations that mix symbolics and numerics. In this article we showcase the basic functionality, highlighting some of the key design choices.

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“…We have recently applied LazySets to compute reachable states for linear wave propagation problems and heat transfer problems [14].…”

Section: Origin Of Lazysets and Current Applicationsmentioning

confidence: 99%

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

2021

JCON

View full text Add to dashboard Cite

show abstract

“…Given this limitation, alternative approaches are mainly based on experimental tests [8] or numerical simulations [42] . Experimental tests might be expensive and/or challenging to design, therefore, new numerical methods for accurate structural dynamics simulations are actively developed [17] .…”

Section: Introductionmentioning

confidence: 99%