Application of Richardson Extrapolation to the Co-Simulation of FMUs from Building Simulation

AbstractWe show that the performances of the finite difference method for double barrier option pricing can be strongly enhanced by applying both a repeated Richardson extrapolation technique and a mesh optimization procedure. In particular, first we construct a space mesh that is uniform and aligned with the discontinuity points of the solution being sought. This is accomplished by means of a suitable transformation of coordinates, which involves some parameters that are implicitly defined and whose existence and uniqueness is theoretically established. Then, a finite difference scheme employing repeated Richardson extrapolation in both space and time is developed. The overall approach exhibits high efficacy: barrier option prices can be computed with accuracy close to the machine precision in less than one second. The numerical simulations also reveal that the improvement over existing methods is due to the combination of the mesh optimization and the repeated Richardson extrapolation.

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Guidelines to Calibrate a Multi-Residential Building Simulation Model Addressing Overheating Evaluation and Residents’ Influence

Buildings ◽

10.3390/buildings11060242 ◽

2021 ◽

Vol 11 (6) ◽

pp. 242

Author(s):

Christoph Schünemann ◽

David Schiela ◽

Regine Ortlepp

Keyword(s):

Simulation Model ◽

Time Window ◽

Residential Building ◽

Simulation Models ◽

Building Simulation ◽

Night Time ◽

Building Performance Simulation ◽

Starting Point ◽

3D Simulation Model ◽

Building Physics

Can building performance simulation reproduce measured summertime indoor conditions of a multi-residential building in good conformity? This question is answered by calibrating simulated to monitored room temperatures of several rooms of a multi-residential building for an entire summer in two process steps. First, we did a calibration for several days without the residents being present to validate the building physics of the 3D simulation model. Second, the simulations were calibrated for the entire summer period, including the residents’ impact on evolving room temperature and overheating. As a result, a high degree of conformity between simulation and measurement could be achieved for all monitored rooms. The credibility of our results was secured by a detailed sensitivity analysis under varying meteorological conditions, shading situations, and window ventilation or room use in the simulation model. For top floor dwellings, a high overheating intensity was evoked by a combination of insufficient use of night-time window ventilation and non-heat-adapted residential behavior in combination with high solar gains and low heat storage capacities. Finally, the overall findings were merged into a process guideline to describe how a step-by-step calibration of residential building simulation models can be done. This guideline is intended to be a starting point for future discussions about the validity of the simplified boundary conditions which are often used in present-day standard overheating assessment.

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