Spatially extended hybrid methods: a review.

Area of Science:

• Computational Science
• Multiscale Modeling
• Scientific Simulation

Background:

• Biological and physical systems often exhibit complex behaviors across multiple scales.
• Simulating these multiscale processes numerically presents significant challenges.
• Coarse methods lack detail, while fine-grained simulations are computationally expensive.

Purpose of the Study:

• To review and compare various spatially extended hybrid methods for multiscale modeling.
• To provide practical examples with algorithms and code for hybrid method implementation.
• To demonstrate the utility of these methods in real-world biological and physical problems.

Main Methods:

• Spatially coupled hybrid methods partition space into subdomains for different modeling approaches.
• These methods allow for multiple representations of species within a single spatial domain.
• The review collates and contrasts existing hybrid techniques.

Main Results:

• A comprehensive collection of spatially extended hybrid methods is presented.
• Canonical examples with algorithms and code illustrate practical applications.
• The utility of hybrid methods is demonstrated through real-world case studies.

Conclusions:

• Spatially coupled hybrid methods offer an effective bridge between coarse and fine-grained simulations.
• This review serves as a valuable resource for selecting and implementing appropriate multiscale hybrid methods.
• Future research directions and open questions in hybrid method development are identified.