# Decoupling PDE Computation with Intrinsic or Inertial Robin Interface Condition

## TL;DR

This paper introduces a novel intrinsic or inertial Robin interface condition for decoupling multi-domain, multi-physics PDE problems, providing a mathematically justified framework that improves numerical decoupling efficiency.

## Contribution

It derives a new interface condition for PDE decoupling that is mathematically and physically justified, enhancing the effectiveness of numerical methods for multi-model problems.

## Key findings

- The new Robin condition improves decoupling accuracy.
- Numerical experiments confirm the effectiveness of the approach.
- The framework generalizes decoupling methods for multi-physics applications.

## Abstract

We study decoupled numerical methods for multi-domain, multi-physics applications. By investigating various stages of numerical approximation and decoupling and tracking how the information is transmitted across the interface for a typical multi-modeling model problem, we derive an approximate intrinsic or inertial type Robin condition for its semi-discrete model. This new interface condition is justified both mathematically and physically in contrast to the classical Robin interface condition conventionally introduced for decoupling multi-modeling problems. Based on the intrinsic or inertial Robin condition, an equivalent semi-discrete model is introduced, which provides a general framework for devising effective decoupled numerical methods. Numerical experiments also confirm the effectiveness of this new decoupling approach.