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Item type:Publication, Access status: without files , Fast algorithms for hp-discretized univariate population balance aggregation integrals(2017-02-02); The efficient numerical simulation of population balance equations requires sophisticated techniques in order to combine accuracy with efficiency. We will focus on the numerical treatment of aggregation integrals that often dominate the overall time in population balance simulations. Following a finite element approach, the density distribution is discretized through a piecewise polynomial of order p > 0 on a nested grid that is refined locally toward an arbitrary point. The proposed method conserves mass while reducing the quadratic complexity (in the dimension of the solution space) of the direct computation to an almost linear complexity. The complexity improvement is based on recursion formulas exploiting orthogonality properties of basis functions along with FFT on locally equidistant portions of the grid. We present numerical results for various initial conditions and provide heuristic criteria for the choice of polynomial degree and grid refinement.Publicationtype: Journal Article170 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Efficient and accurate evaluation of aggregation integrals in population balance equations(2017); Applications of population balance equations can be found in many chemical production processes, e.g, crystallization and precipitation of pharmaceutical materials. In population balance equations the aggregation process is described by source and sink aggregation integrals. The source aggregation integral is usually numerically expensive to evaluate having quadratic complexity. In this thesis we focus on the efficient and accurate evaluation of aggregation integrals, reducing this complexity to almost linear. We also include extensive numerical tests for different setups, leading to (heuristic) strategies for the choice of the discretization parameters.Publicationtype: Doctoral Thesis475 450 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Algorithms for the Haar wavelet based fast evaluation of aggregation integrals in population balance equations(2016-10-01); In several production processes, the distribution of particles dispersed in an environmental phase may be mathematically described by the solution of population balance equations. We are concerned with the development of efficient numerical techniques for the aggregation process: It invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost. We describe an approach on locally refined nested grids to evaluate both the source and the sink terms in almost linear complexity (instead of quadratic complexity resulting from a direct approach). The key is to switch from a nodal to a wavelet basis representation of the density function. We illustrate the numerical performance of this approach, both in comparison to a discretization of piecewise constant functions on a uniform grid as well as to the fixed pivot method on a geometric grid.Publicationtype: Journal Article119 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Fast evaluation of univariate aggregation integrals on equidistant grids(2015-03-04); ; A variety of production processes in chemistry and biotechnology are concerned with particles dispersed in an environmental phase. The particle distribution is mathematically described by the solution of population balance equations of integro-differential type. We are concerned with the aggregation process: it invokes an integral term that is usually numerically expensive to evaluate and often dominates the total simulation cost. We will expose the algorithmic details of an efficient approach based on a separable approximation of the aggregation kernel and a subsequent fast Fourier transformation. This approach reduces the originally quadratic complexity to an almost optimal complexity O(nlogn) in the dimension of the approximation space. We include numerical tests illustrating its application to representative aggregation kernels from the literature. While originally developed in the context of a discretization with piecewise constant functions, we illustrate how these ideas can be applied in the setting of the popular sectional methods.Publicationtype: Journal Article114