Moment-inversion algorithm direct

When the first procedure is adopted, the CQMOM should be used as the moment-inversion algorithm (Yuan Fox, 2011). When the second procedure is adopted, the evolution of the M-dimensional, iV-point quadrature approximation is directly tracked. In the case of spatially homogeneous systems the two methods are equivalent. 

The quadrature method of moments (QMOM) and the direct quadrature method of moments (DQMOM) were introduced in Chapter 3 as equivalent methods for solving a homogeneous GPBE. In fact, the DQMOM was derived by Marchisio Fox (2005) primarily for the purpose of solving spatially inhomogeneous multivariate moment-transport equations. Unlike for the univariate case, where the moment-inversion algorithm is uniquely defined for a given set of moments, the QMOM in the multivariate case is much... 

Chapter 3 provides an introduction to Gaussian quadrature and the moment-inversion algorithms used in quadrature-based moment methods (QBMM). In this chapter, the product-difference (PD) and Wheeler algorithms employed for the classical univariate quadrature method of moments (QMOM) are discussed, together with the brute-force, tensor-product, and conditional QMOM developed for multivariate problems. The chapter concludes with a discussion of the extended quadrature method of moments (EQMOM) and the direct quadrature method of moments (DQMOM). 

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