Free boundary problems can be reformulated as shape optimization problems with partial differential equation (PDE) constraints, making them solvable through numerical shape optimization algorithms. The Smooth Extension Embedding Method (SEEM), a novel approach for solving PDEs, leverages straightforward discretization of complex domains and achieves a high degree of convergence for problems with smooth solutions. This makes SEEM a viable alternative to the finite element methods used in traditional numerical shape optimization algorithms, effectively overcoming key challenges such as mesh degeneration and low-order convergence. To enhance the stability of SEEM while maintaining its high-order accuracy for boundary value problems on non-smooth numerical representations of inherently smooth boundaries, we employ a regularized level set boundary approximation technique. This enhancement broadens the applicability of SEEM to the class of free boundary problems with a shape optimization approach. Through theoretical and practical examples, experiments show that our improved SEEM-based algorithm maintains high-order accuracy in shape gradient approximation and circumvents computational pitfalls like mesh degeneration that can arise during shape evolution. This makes the direct use of a simple shape gradient formula and an explicit gradient descent flow possible. The resulting algorithm employs straightforward domain grids throughout the shape optimization process, resulting in significant computational savings and ease of implementation.

This dissertation offers a new narrative on the history of public debt in late Qing and Republican-era China (1850 – 1914), highlighting its links with late Qing and Republican political economy. A history of economic ideas and institutions, the dissertation draws from official and diplomatic communications, contemporary newspapers and journals, academic studies and private letters to explore the process of its embedment into Chinese fiscal system and its evolution in China as a set of discourses and practice, including its reception by officials, merchants and general public, and its adjustment to established discourses of political economy in late Qing and Republican China.

Adopting an expansive conception of public debt to include related public credit mechanisms and discourses, the dissertation traces the impact of pre-1850 official debates on late 19th Century Chinese officials’ ambivalence towards modern public debt. It argues that a domestic intellectual and policy reorientation in favour of growth was needed and mostly achieved before Qing’s military defeat in 1895, paving the way for large-scale borrowing that in turn reconfigured state-society relations in late Qing. The dissertation also investigates how mid-Victorian liberal discourses on public debt were co-opted by Chinese reformists, which in their modified form of political and fiscal accountability, proved to be effective in dominating late Qing and Republican discourses on public debt.

This dissertation is one of the first English-language studies discussing the evolution of economic ideas surrounding Chinese public debt. Recounting China’s historical experiences with public debt, and discourses on political economy that resulted from these experiences would promote a more layered understanding of public debt’s role for peripheral economies in the late 19th and 20th Century.