While the basis splines (B-splines) have been employed to construct the sparse-grid quadrature or interpolation, including those associated with a hierarchical version , they are neither orthogonal nor measure-consistent, meaning that the basis functions are not adapted to the probability measure of input random variables.
Ma2 multipatch how to#
For the stochastic collocation methods, the crucial factor is how to construct the set of collocation points appropriately because the choice of the collocation points determines the performance of the method. For practical engineering problems mandating expensive-to-run computational analysis, MCS is hardly feasible or affordable. Although MCS is popular owing to its simplicity, broad applicability, and natural suitability for parallel computing, it is often subject to slow convergence. UQ often requires solving stochastic partial differential equations (PDEs) by numerical methods, such as Monte Carlo simulation (MCS) as a direct sampling method, stochastic finite element methods , stochastic boundary-element methods , stochastic meshfree methods ,, non-intrusive sparse-grids methods , collocation methods , and so forth. This process, referred to as uncertainty quantification (UQ), entails effectively propagating uncertainties from input to an output response variable of interest. Uncertainties in the output are generally dependent on those of the input, and must be quantified accurately for meticulous design of complex systems. In such a case, if a stress response is defined as an output function, the response variable is naturally random as well. For instance, consider a system where some material properties, geometrical characteristics, and external loads are random based on the nature of the manufacturing processes and operational conditions. Many complex mechanical systems exhibit uncertainties in their responses due to the intrinsic uncertainties in the input to the system. Numerical results, including those obtained for a 54-dimensional, industrial-scale problem, demonstrate that a low-order SDD-mIGA is capable of efficiently delivering accurate probabilistic solutions when compared with the benchmark results from crude Monte Carlo simulation.
Analytical formulae have been derived to calculate the second-moment properties of an SDD-mIGA approximation for a general output random variable of interest. The proposed method can handle arbitrary multipatch domains in IGA and uses standard least-squares regression to efficiently estimate the SDD expansion coefficients for uncertainty quantification applications. The method, referred to as SDD-mIGA, involves (1) analysis-suitable T-splines with significant approximating power for geometrical modeling, random field discretization, and stress analysis (2) Bézier extraction operator for isogeometric mesh refinement and (3) a novel Fourier-like expansion of a high-dimensional output function in terms of measure-consistent orthonormalized splines. Technical specifications as specified in the data sheet unless noted otherwise in the order.This paper presents a new stochastic method by integrating spline dimensional decomposition (SDD) of a high-dimensional random function and isogeometric analysis (IGA) on arbitrary multipatch geometries to solve stochastic boundary-value problems from linear elasticity. – Including a 2 years maintenance package (software updates and support) – Advanced trigger settings, Multi File Mode and extended Multi File Mode
Ma2 multipatch free#
– Free assignment of trigger inputs/outputs to analog outputs
Ma2 multipatch download#
– Design, import (ASCII), and download of complex stimulus pulses to the STG – Digital I/O-port (8 bit input, 8 bit output) – 8 trigger (TTL) outputs (BNC connector) – 8 analog current outputs: -16 mA to +16 mA 120 V (2 mm connector) – 8 analog voltage outputs: -8 V to +8 V ☒0 mA (2 mm connector)
Operating in Download and Streaming mode (continuous downstreaming of pulses from connected computer). 8-channel general-purpose stimulus generator for current and voltage-driven electrical stimulation, 4000 series, with integrated stimulus isolation unit for each output channel.