PDE-Based Optimization for Advection Diffusion Equation in 2D Domain

TL;DR

This paper introduces a PDE-based optimization approach for microfluidic heat transfer, utilizing spectral methods to efficiently find optimal velocity fields in 2D, with theoretical insights provided.

Contribution

It presents a novel spectral method-based PDE optimization framework for 2D advection-diffusion problems, reducing complexity and improving accuracy.

Findings

Reduced computational complexity of PDE optimization

Enhanced accuracy in approximating PDE solutions

Theoretical results supporting the method

Abstract

In this paper, we propose a PDE-based optimization motivated by the problem of microfluidic heat transfer to finding the optimal incompressible velocity fields in 2D domain. To solve this optimization model, we use spectral method to discretize the model to obtain an ODE based optimization. This way significantly reduces the complexity of the discretization optimization model, and gives a more accurate approximation of the original PDE based optimization. Some theoretical results are obtained.