Matrix solvers using GPU 
Bottlenecks: complexity, ill-condition, parallel processing
Preconditioning + CG + ridge regression + random process

Simulation with variations
Bottlenecks: complexity, Monte Carlo iterations

Power ground + thermal + stress anlaysis 
Bottlenecks: complexity, limited margines, resolutions vs precision

X parameter analysis
Bottlenecks: convergency

Matrix exponential process
Bottlenecks: Theory for nonlinear systems
Possible Direction: Rosenbrock, Richardson methods
References: M. Hochbruck, A. Ostermann, N.J. Higham

Multiple scale simulation
Bottlenecks: High complexity in time (multiple rates) and space (multiple grids)
Possible Direction: spatial/temporal variable splitting
References: Jiun-Shyan Chen, H.G. Brachtendorf, J.C. Pedro, J. Roychowdhury

Stimulus generation
Bottlenecks: complexity, worst case analysis
Possible Direction: dynamic programming
References: R. Shi, CK Cheng, B. Casper, F.N. Najm

Full wave analysis
Bottlenecks: complexity
Possible Direction: Krylov space methods, FFT
References: D. Jiao, Q. He, AE Yilmaz,