High-performance computing has played a key role in GMIG’s collaborations with corporate partners in Houston’s energy sector and beyond. Longstanding bedrocks of the group’s research, mathematics and algorithmic development have remained foundational to GMIG even as the program has expanded into a wide range of subjects and applications.

GMIG’s algorithms and software have been focused on massively parallel direct structured solvers, preconditioners and eigensolvers. Its fast-updating algorithms have been essential in working with computational inverse problems. Common discretization is based on unstructured tetrahedral meshes and encoding shapes associated with any possible segmentation through level sets. GMIG made early contributions to the field of randomized numerical linear algebra, with applications ranging from high-frequency computing, time-harmonic acoustic waves, elastic waves, guided waves and normal modes in rotating planets.

GMIG’s program on computational seismology focuses on solving acousto-elastic (with fluid-solid boundaries), poro-elastic and visco-elastic wave equations, and (nonlinear) dynamic rupturing through iterative coupling. The entire elastic-gravitational system of equations is employed in the computation of normal modes. Recently, GMIG has designed an algorithm of viscoelastic and tidal deformation that considers the extended Burgers model. The group’s focus has now shifted toward deep-learning-based approaches involving neural operators and global neural networks.

Further reading: Fast factorization update for general elliptic equations under multiple coefficient updates