The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which are independent of the mesh sizes and are independent of jumps in the coefficients (BNN). Here w...

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to flattest local minimizer can be found due implicit regularization of stochastic gradient descent. This paper proposes network-based structure probing deflation method make deep capable identifying multiple solutions that are ubiquitous and important in physical models. ...

Phospholipid-coated ultrasound contrast agents may deflate or even collapse because of stress resulting from ultrasound-induced oscillations. In this work we investigate the behavior of isolated contrast agent microbubbles during prolonged ultrasound excitation. Isolated microbubbles placed in a thin capillary tube were excited with hundreds of ultrasound pulses at a low mechanical index, and t...

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