This Small Business Innovation Research (SBIR) Phase I project addresses the need for improved block trading capabilities in the financial markets. Block trading, or sell-side trading, involves transacting large blocks of stock (for example, 450,000 shares of IBM), while trying to minimize market impact and receive the best price for the stock. Block-trading technology is necessary for institutions holding large positions in equities. Much of the current block-trading technology is inefficient and expensive, often being done by hand or by very simple software systems. The research proposed here will leverage Benchmark's expertise in diffusive systems and high-frequency trading technology. Benchmark's proposed block-trading system will reduce market impact, lower transaction costs, and improve returns for institutions making large block trades. The potential commercial value of an advanced block-trading system is substantial and global. Also, fundamental advances in spacetime finite element inversion associated with this research may have broader application to numerical simulation in other fields