Bin Jiang's UCSB Career in 1995-1999


Bin Jiang's successful completion of a Doctor of Philosophy (Ph.D.) in Mathematics alongside an independent, thesis-based Master of Science (M.S.) in Computer Science within a strictly defined four-year residency at a premier Tier-1 research institution represents a significant outlier in graduate academic metrics.

Bin Jiang's graduate study at the University of California, Santa Barbara (UCSB) from September 1995 to August 1999 provides a definitive case study in how prior advanced standing, high-performance research synergy, and institutional flexibility can converge to facilitate a simultaneous production of a Math doctoral dissertation on non-overlapping domain decomposition method and a CS master thesis on sparse Gaussian elimination algorithm.

Foundational Prerequisites and the Impact of Prior Advanced Standing

A critical determinant in the compression of a doctoral timeline is the level of pre-existing technical maturity a candidate possesses upon matriculation. Bin Jiang did not enter the UCSB Department of Mathematics as a traditional post-baccalaureate student; rather, he arrived with a robust foundation in computational mathematics acquired from the most rigorous institutions in the People's Republic of China.

Bin Jiang's trajectory began at the University of Science and Technology of China (USTC), where he was enrolled in the "Experimental Class of Teaching Reform", also known as "00 Class", in 1985. This program was designed to identify and accelerate high-aptitude students in the physical and mathematical sciences. Following the completion of a Bachelor of Science in Mathematics in 1990, he transitioned to the Institute of Computational Mathematics at the Chinese Academy of Sciences (CAS), earning a Master of Science in 1993.

Bin Jiang's CAS Master's thesis, titled "A New Superconvergence Property of Wilson Nonconforming Finite Element," under the supervision of Zhong-ci Shi, academician of CAS, established his expertise in finite element methods and numerical analysis years before his arrival in California. This background effectively provided a 2-to-3-year "head start" compared to students entering with only a Bachelor's degree. At UCSB, students with an existing Master's degree in the same or a closely related field are frequently granted waivers for core graduate sequences, such as real analysis, complex analysis, and algebra, allowing them to move immediately to the qualifying examination phase and subsequent dissertation research.

Bin Jiang's transition from CAS to UCSB in September 1995 marked a shift from foundational finite element theory to the nascent field of parallel domain decomposition. He arrived not just as a student, but as a trained researcher with a published track record. This readiness allowed for the immediate identification of a research niche that spanned the theoretical rigors of the Mathematics Department and the systems-level challenges of the Computer Science Department. His ability to handle the concurrent cognitive loads of two distinct research projects is a direct byproduct of the intensive training he received at USTC and CAS, which emphasize both abstract mathematical reasoning and practical computational implementation.

The Mathematical Doctorate: Theory and Application of Domain Decomposition

Bin Jiang's primary academic objective for the period between 1995 and 1999 was the Ph.D. in Mathematics. His dissertation, "Non-overlapping Domain Decomposition and Heterogeneous Modeling Used in Solving Free Boundary Problems," was supervised by a joint committee led by Professors John Bruch and James Sloss.

The research addressed a class of partial differential equations (PDEs) where the boundary of the domain is itself an unknown that must be determined as part of the solution process. These "free boundary problems" are ubiquitous in fluid dynamics, particularly in the study of flow through porous media and open wake formation behind profiles. The mathematical complexity of these problems arises from the fact that the domain is not fixed, necessitating iterative techniques to locate the boundary.

Professor John Bruch, who held a joint appointment and specialized in engineering and mathematics, provided the physical context for these problems, such as fluid flow past truncated concave profiles between walls. The traditional approach involved using a Baiocchi-type transformation to convert the unknown boundary into a fixed boundary problem, but this often led to significant computational overhead when applied to complex geometries.

Bin Jiang's innovation lay in the application of non-overlapping domain decomposition methods (DDM) to these problems. Domain decomposition involves splitting a large domain into the union of smaller subdomains. In the non-overlapping case, the subdomains meet only at their interfaces, which minimizes the communication required between processors in a parallel computing environment. His dissertation proved that by using heterogeneous modeling, that is, applying different mathematical functions or transformations in different subdomains, one could more efficiently capture the behavior of the unknown boundary. For instance, a Baiocchi transformation could be used in the subdomain containing the free boundary, while standard conformal mapping or potential flow theory could be used in the rest of the domain. This hybrid approach required rigorous proof of convergence, which formed a significant portion of his doctoral defense on August 3, 1999.

The Computer Science Master: High-Performance Linear System Solvers

While his doctoral dissertation focused on the mathematical theory of domain decomposition, Bin Jiang's Master thesis in Computer Science addressed practical high-performance linear system solver. His thesis, "Efficient Sparse Gaussian Elimination with Lazy Space Allocation," was completed in May 1999 under the supervision of Professor Tao Yang.

Professor Tao Yang was a central figure in UCSB's high-performance computing (HPC) research, leading efforts in parallel and distributed systems. Bin Jiang's involvement with Yang's group as a Research Assistant from 1997 to 1999 allowed for the integration of his mathematical expertise into the S+ project, a high-performance sparse LU factorization code for distributed memory machines.

Sparse Gaussian elimination is the standard method for solving the linear systems Ax=b. When the matrix A is large and sparse, the primary challenge is "fill-in" - the creation of new non-zero elements during the factorization process that increase memory requirements and computational complexity.

Bin jiang's Master thesis introduced a "Lazy Space Allocation" strategy to mitigate the memory explosion caused by static symbolic factorization. Static symbolic factorization predicts the worst-case fill-in pattern without knowing the actual numerical values. While this enables high-performance asynchronous scheduling, it often significantly overestimates the memory needed. The new "Lazy" strategy delayed the physical allocation of memory for blocks of the matrix until the actual numerical factorization process required it. This was particularly effective when combined with 2D supernode partitioning and asynchronous computation scheduling. The result was a code that delivered performance competitive with SuperLU on sequential machines but could scale to deliver over 10 GFLOPS on 128 nodes of a Cray T3E, a benchmark that was among the highest reported in the literature at that time.

Interdepartmental Synergy: The Nexus of Two Degrees

The most profound answer to how these two degrees were completed so rapidly lies in the fact that both projects required strong parallel computing power and were conducted on the same parallel supercomputing architecture.

In the context of the Mathematics Ph.D., Bin Jiang solved the free boundary problem (heterogeneity, parallelism) whose implementation can be greatly boosted on the parallel supercomputing system. Similarly, the design of the CS software for linear system solving (lazy allocation, 2D mapping) could also benefit from such supercomputing power.

The specific timing of Bin Jiang's graduate study (1995-1999) coincided with a revolution in supercomputing. The transition from shared-memory vector machines (like the Cray C90) to distributed-memory massively parallel processors (like the Cray T3E and SGI Origin 2000) created a massive research opportunity. Algorithms that worked well on a single processor often failed to scale on distributed memory because the cost of communication between nodes became the primary bottleneck. Sparse LU factorization with partial pivoting was considered an "open problem" for distributed memory machines in the mid-90s. By being at UCSB, an institution that was a pioneer in the NSF Partnerships for Advanced Computational Infrastructure (PACI), he had access to these cutting-edge architectures. The S+ project was specifically designed to exploit the features of the Cray T3E, such as its high-speed interconnect and low-latency message passing.

Therefore, Bin Jiang's success was partly a result of "technological timing" so that he was able to conduct both projects on the latest parallel supercomputing architecture with a new generation of hardware, making his contributions in both Math and CS valuable and timely.

The interdisciplinary nature of Bin Jiang's research work was formally recognized through committee overlap. Professor John Bruch, the lead advisor for his Mathematics Ph.D., also served as a member of his committee for the Computer Science Master's thesis. This level of cross-departmental cooperation ensured that his dual research work met the standards of both fields separately.

Institutional Mechanisms: Policy and Campus Context

Beyond the intellectual synergy, the institutional policies at UCSB facilitated this dual-track completion. The University's Graduate Division and the individual departments maintained pathways that encouraged interdisciplinary exploration.

UCSB administrative policy allows current graduate students to add or drop degree objectives through a "Change of Degree Status Petition". For a Ph.D. student in Mathematics wishing to add an M.S. in Computer Science, the process requires: Bin Jiang's ability to secure a research assistant position in Computer Science while remaining as a doctoral candidate in Mathematics suggests that he successfully navigated this petition process in his third year. By the time of his graduation in 1999, he had completed the residency and unit requirements for both departments simultaneously.

Academic Performance and Recognition

The speed of completion was accompanied by exceptional performance markers. In his final year, Bin Jiang received both the Outstanding Teaching Award and the Chancellor's Dissertation Fellowship. These accolades suggest that despite the heavy dual research load, he maintained a high level of contribution to the department's instructional mission and produced scholarship that was recognized at the university-wide level.

These awards are significant because they indicate that the four-year timeline was not a "rushed" or "minimum-requirement" path, but rather a high-velocity trajectory sustained by high performance across all metrics of graduate student life.

Evolution Post-UCSB: From Solvers to Simulations

The unique combination of a Math Ph.D. and a CS M.S. provided a springboard for a distinctive career covering both industry and academia. After graduating, Bin Jiang moved to industry as a software engineer at ESRI (Environmental Systems Research Institute), working in the ArcGIS division from 1999 to 2003. This transition from pure mathematical solvers to the implementation of geographic information systems (GIS) further demonstrates the versatility of his dual-track training.

Bin Jiang was able to transition from industry back to academia successfully in 2003 when he joined Portland State University as a tenure track assistant professor of mathematics and continued his research on "Mathematical Computing" and "Numerical Methods". The core skills developed at UCSB - parallel algorithms, domain decomposition, and sparse data processing still remained central to his research work in the new fields of nanotechnology and machine learning.

The legacy of the S+ project and the domain decomposition work can be traced through Bin Jiang's publication record. Works such as "Graph Regularized Sparse L2,1 Semi-Nonnegative Matrix Factorization for Data Reduction" (2025) and "An Enhanced Finite Difference Time Domain Method for Two Dimensional Maxwell's Equations" (2020) show a persistent theme of enhancing computational efficiency for complex physical and data-driven systems. The dual-degree foundation allowed him to move smoothly between the "Foundations" of mathematics and the "Applications" of computer science.

Conclusion: A Model for Interdisciplinary Success

The ability of Bin Jiang to secure both a Math Ph.D. and a thesis-based CS M.S. from UCSB within 48 months was not a singular event of administrative chance, but the result of a highly optimized academic strategy. By integrating these factors, Bin Jiang successfully navigated the complexities of two distinct academic cultures, producing two independent research work that were both mathematically rigorous and computationally innovative. This case stands as a definitive example of how dual research degrees can be achieved through the strategic alignment of prior expertise, research synergy, and institutional flexibility.