A strongly S-stable low-dissipation and low-dispersion Runge-Kutta scheme for convection diffusion systems

Du, Yongle; Liu, Yanchen

doi:10.1016/j.ast.2019.105355

“…In addition, when a fixed step-size is used, strongly S -stable methods are more accurate than the other methods. Several numerical tests showed that only S -stable methods can produce accurate simulations by using significantly large step-size for stiff problems [73]. Finally, RADAU5 is capable of arranging the step-size along with the desired error—controlled by means of ε a and ε r tolerances, which are user-defined parameter—and the detected level of stiffness.…”

Section: Methodsmentioning

confidence: 99%

FiCoS: a fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

Tangherloni

¹

,

Nobile

²

,

Cazzaniga

³

et al. 2021

Preprint

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Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can then be tested with targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring when rule-based models are analysed. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel “black-box” deterministic simulator that effectively realizes both a fine- and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely the Dormand–Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855 ×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.Author summarySystems Biology is an interdisciplinary research area focusing on the integration of biology and in-silico simulation of mathematical models to unravel and predict the emergent behavior of complex biological systems. The ultimate goal is the understanding of the complex mechanisms at the basis of biological processes together with the formulation of novel hypotheses that can be then tested with laboratory experiments. In such a context, detailed mechanistic models can be used to describe biological networks. Unfortunately, these models can be characterized by hundreds or thousands of molecular species and chemical reactions, making their simulation unfeasible using classic simulators running on modern Central Processing Units (CPUs). In addition, a large number of simulations might be required to calibrate the models or to test the effect of perturbations. In order to overcome the limitations imposed by CPUs, Graphics Processing Units (GPUs) can be effectively used to accelerate the simulations of these detailed models. We thus designed and developed a novel GPU-based tool, called FiCoS, to speed-up the computational analyses typically required in Systems Biology.

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“…In addition, when a fixed step-size is used, strongly S -stable methods are more accurate than the other methods. Several numerical tests showed that only S -stable methods can produce accurate simulations by using significantly large step-size for stiff problems [ 73 ]. Finally, RADAU5 is capable of arranging the step-size along with the desired error—controlled by means of ε a and ε r tolerances, which are user-defined parameters—and the detected level of stiffness.…”

Section: Methodsmentioning

confidence: 99%

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

Tangherloni

¹

,

Nobile

²

,

Cazzaniga

³

et al. 2021

View full text Add to dashboard Cite

Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel “black-box” deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand–Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.

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An improved class of three stage low-dispersion low-dissipation diagonally implicit Runge-Kutta method

Giri¹,

Sen²

2023

Aerospace Science and Technology

1

0

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A strongly S-stable low-dissipation and low-dispersion Runge-Kutta scheme for convection diffusion systems

Cited by 4 publications

References 31 publications

FiCoS: a fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

FiCoS: a fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

An improved class of three stage low-dispersion low-dissipation diagonally implicit Runge-Kutta method

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