Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
A multigrid tutorial: second edition
A multigrid tutorial: second edition
A variational finite element method for source inversion for convective-diffusive transport
Finite Elements in Analysis and Design - Special issue: 14th Robert J. Melosh competition
V-cycle convergence of some multigrid methods for ill-posed problems
Mathematics of Computation
Finite Elements in Analysis and Design
SIAM Journal on Scientific Computing
Hessian-Based Model Reduction for Large-Scale Data Assimilation Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Optimization under adaptive error control for finite element based simulations
Computational Mechanics
Fast Algorithms for Source Identification Problems with Elliptic PDE Constraints
SIAM Journal on Imaging Sciences
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Dynamic Data Driven Application System for Plume Estimation Using UAVs
Journal of Intelligent and Robotic Systems
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In contrast to traditional terascale simulations that have known, fixed data inputs, dynamic data-driven (DDD) applications are characterized by unknown data and informed by dynamic observations. DDD simulations give rise to inverse problems of determining unknown data from sparse observations. The main difficulty is that the optimality system is a boundary value problem in 4D space-time, even though the forward simulation is an initial value problem. We construct special-purpose parallel multigrid algorithms that exploit the spectral structure of the inverse operator. Experiments on problems of localizing airborne contaminant release from sparse observations ina regional atmospheric transport model demonstrate that 17-million-parameter inversion can be effected at a cost of just 18 forward simulations with high parallel efficiency. On 1024 Alphaserver EV68 processors, the turnaround time is just 29 minutes. Moreover, inverse problems with 135 million parameters - corresponding to 139 billion total space-time unknowns - are solved in less than 5 hours on the same number of processors. These results suggest that ultra-high resolution data-driven inversion can be carried out sufficiently rapidly forsimulation-based "real-time" hazard assessment.