# Fast volumetric integral equation solvers and applications

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · William Marsh Rice University (TX) · $343,612

## Abstract

The ability to efficiently conduct high-fidelity simulations of complex physical phenomena simultaneously reflects our increased understanding of the underlying physics and enables future technological developments based on rapid iterative/inverse design. This project concerns a class of simulation techniques that rely on fundamental solutions (that is, by expressing solutions as a complicated superposition of `point sources' of light, sound, etc.) which have been highly effective when applicable as they have enabled transformational simulations of problems in electrostatics, wave phenomena as well as in human blood flow contexts. But more complicated phenomena (e.g. featuring nonlinearities or spatially-varying media), which are increasingly relevant in applications in medical imaging and also have long-standing intrinsic importance in geophysical exploration, have posed a substantial barrier to this class of methods---which thus have significant untapped potential in these application domains. This project will develop numerical methods with rigorous approximation guarantees to solve these physical problems and enable new scientific questions to be answered / for new technology to be designed, thereby strengthening the U.S. competitiveness and national defense. On the education front, the project will involve training in modern scientific computing generally and for their use in integral equation methods and applied to wave propagation particularly, all rare skills highly 

## Key facts

- **NSF award ID:** 2514012
- **Awardee organization:** William Marsh Rice University (TX)
- **SAM.gov UEI:** K51LECU1G8N3
- **PI:** Thomas G Anderson
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** COMPUTATIONAL SCIENCE & ENGING
- **Estimated total:** $343,612
- **Funds obligated:** $343,612
- **Transaction type:** Standard Grant
- **Period:** 07/01/2025 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2514012

## Citation

> US National Science Foundation, Award 2514012, Fast volumetric integral equation solvers and applications. Retrieved via AI Analytics 2026-06-08 from https://api.ai-analytics.org/grant/nsf/2514012. Licensed CC0.

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