MWRtools: a library for weighted residual method calculations

Lin, Yu‐Min; Chang, Hsiao-Yung; Adomaitis, Raymond A.

doi:10.1016/s0098-1354(99)00272-0

Cited by 18 publications

(11 citation statements)

References 17 publications

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“…Representative simulation results are presented in Fig. 5; details of solution convergence assessment are presented in [17]. The simulation results presented here corroborate with published experimental observations of axial compressor stall [19].…”

Section: Process Gas Compression -Galerkin Pseudo-spectral Methodssupporting

confidence: 83%

A Computational Framework for Boundary-Value Problem Based Simulations

2000

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ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, distributed-parameter system models. Four industrially relevant examples taken from electronic materials and chemical processing applications are used to demonstrate the simulation approach developed.

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Section: Process Gas Compression -Galerkin Pseudo-spectral Methodssupporting

confidence: 83%

A Computational Framework for Boundary-Value Problem Based Simulations

2000

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“…Accurate and efficient algorithms for determining the Jacobi polynomial roots and the associated quadrature weights w have been developed (e.g., [8,9]); however, these algorithms can be modified to improve their numerical accuracy and efficiency, and to take advantage of vectorized computational operations [10]. In the first step of our algorithm, points are placed in the unit interval at locations that approximate the spacing of Jacobi polynomial roots of degree significantly higher than M (we use the extrema of a (3M − 1)-degree Chebyshev polynomial because they can be computed explicitly).…”

Section: Collocation Points and Quadrature Weightsmentioning

confidence: 99%

“…Details regarding the quadrature weight formula derivations and numerical methods developed to overcome additional computational limitations can be found in [10]. We have found that accurate computations can be performed using over M = 500 discretization points.…”

Section: Collocation Points and Quadrature Weightsmentioning

confidence: 99%

“…The eigenfunctions Ψ are interpolated to this finer grid, using the Lagrange interpolation functions. Because it is computationally difficult to use the interpolation polynomials directly in cases of high-degree discretizations, we use Neville's algorithm [13] and other computational techniques that avoid direct evaluation of high-degree Jacobi polynomials for interpolation [10].…”

Section: Error Controlmentioning

confidence: 99%

“…We have implemented the collocation-based Sturm-Liouville problem solving procedure as part of a Matlabbased set of computational tools for solving boundary-value problems by the method of weighted residuals [10]. The eigenvalue, eigenfunction, and weight arrays are generated by the function…”

Section: Computational Examplesmentioning

confidence: 99%

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A collocation/quadrature-based Sturm–Liouville problem solver

Adomaitis

Lin

2000

Applied Mathematics and Computation

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ISR develops, applies and teaches advanced methodologies of design and analysis toKeywords: Sturm-Liouville problems; collocation; quadrature; eigenfunction expansions; computational methods. AbstractWe present a computational method for solving a class of boundary-value problems in Sturm-Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfunctions that produce residuals exceeding an infinity-norm bound are discarded. Because the computational approach involves the generation of quadrature weights and discrete differentiation operations, our computational methods provide a convenient framework for solving boundary-value problems by eigenfunction expansion and other projection methods.

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Effects of External Mass Transfer and Product Inhibition on a Simulated Immobilized Enzyme‐Catalyzed Reactor for Lactose Hydrolysis

Al-Muftah

Abu-Reesh

2004

Engineering in Life Sciences

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A mathematical model has been developed for predicting the performance and simulation of a packed bed immobilized enzyme reactor performing lactose hydrolysis, which follows Michaelis‐Menten kinetics with competitive product (galactose) inhibition. The performance characteristics of a packed bed immobilized enzyme reactor have been analyzed taking into account the effects of various diffusional phenomena like axial dispersion and external mass transfer limitations. The model design equations are then solved by Galerkin's method and orthogonal collocation on finite elements. The effects of external mass transfer and axial dispersion have been studied and their effects were shown to reduce the external effectiveness factor. The effects of product inhibition have been investigated at different operating conditions correlated at different regimes using dimensionless moduli (St, γ, θ, Da)1). The product inhibition was shown to reduce the substrate conversion, and, additionally, to decrease the effectiveness factor when Da > Daxo, however, it increases the effectiveness factor when Da < Daxo. The effectiveness factor is found to be independent of the product inhibition at a crossover point at which Daxo is defined. Effects of St and Pe have been investigated at different kinetic regimes and the results show that their effects have a strong dependency on the kinetic parameters θ, γ (i.e., Km/Kp), and Daxo.

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MWRtools: a library for weighted residual method calculations

Cited by 18 publications

References 17 publications

A Computational Framework for Boundary-Value Problem Based Simulations

A Computational Framework for Boundary-Value Problem Based Simulations

A collocation/quadrature-based Sturm–Liouville problem solver

Effects of External Mass Transfer and Product Inhibition on a Simulated Immobilized Enzyme‐Catalyzed Reactor for Lactose Hydrolysis

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