TY - GEN A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy Compression for Large Scale PDE Problems N2 - Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives. T3 - ZIB-Report - 19-32 KW - partial differential equation KW - data compression KW - floating point compression KW - lossy compression Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-73817 SN - 1438-0064 ER - TY - JOUR A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Compression Challenges in Large Scale Partial Differential Equation Solvers JF - Algorithms N2 - Solvers for partial differential equations (PDEs) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that need to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to the relatively small arithmetic intensity, and increasingly due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers over the recent decades. This paper surveys data compression challenges and discusses examples of corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to the main memory. We illustrate concepts for particular methods, with examples, and give references to alternatives. Y1 - 2019 U6 - https://doi.org/10.3390/a12090197 VL - 12 IS - 9 SP - 197 ER - TY - GEN A1 - Schneck, Jakob A1 - Weiser, Martin A1 - Wende, Florian T1 - Impact of mixed precision and storage layout on additive Schwarz smoothers N2 - The growing discrepancy between CPU computing power and memory bandwidth drives more and more numerical algorithms into a bandwidth- bound regime. One example is the overlapping Schwarz smoother, a highly effective building block for iterative multigrid solution of elliptic equations with higher order finite elements. Two options of reducing the required memory bandwidth are sparsity exploiting storage layouts and representing matrix entries with reduced precision in floating point or fixed point format. We investigate the impact of several options on storage demand and contraction rate, both analytically in the context of subspace correction methods and numerically at an example of solid mechanics. Both perspectives agree on the favourite scheme: fixed point representation of Cholesky factors in nested dissection storage. T3 - ZIB-Report - 18-62 KW - higher order finite elements KW - mixed precision KW - overlapping Schwarz smoother Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71305 SN - 1438-0064 ER - TY - GEN A1 - Özel, M. Neset A1 - Kulkarni, Abhishek A1 - Hasan, Amr A1 - Brummer, Josephine A1 - Moldenhauer, Marian A1 - Daumann, Ilsa-Maria A1 - Wolfenberg, Heike A1 - Dercksen, Vincent J. A1 - Kiral, F. Ridvan A1 - Weiser, Martin A1 - Prohaska, Steffen A1 - von Kleist, Max A1 - Hiesinger, Peter Robin T1 - Serial synapse formation through filopodial competition for synaptic seeding factors N2 - Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses. T3 - ZIB-Report - 19-45 KW - filopodia KW - growth cone dynamics KW - brain wiring KW - 2-photon microscopy KW - model Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74397 SN - 1438-0064 ER - TY - JOUR A1 - Ozel, Mehmet Neset A1 - Kulkarni, Abhishek A1 - Hasan, Amr A1 - Brummer, Josephine A1 - Moldenhauer, Marian A1 - Daumann, Ilsa-Maria A1 - Wolfenberg, Heike A1 - Dercksen, Vincent J. A1 - Kiral, Ferdi Ridvan A1 - Weiser, Martin A1 - Prohaska, Steffen A1 - von Kleist, Max A1 - Hiesinger, Peter Robin T1 - Serial synapse formation through filopodial competition for synaptic seeding factors JF - Developmental Cell N2 - Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a 'serial synapse formation' model, where at any time point only a single 'synaptogenic' filopodium suppresses the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation, which is sufficient to cause the destabilization of entire axon terminals. Our model provides a filopodial 'winner-takes-all' mechanism that ensures the formation of an appropriate number of synapses. Y1 - 2019 U6 - https://doi.org/10.1016/j.devcel.2019.06.014 VL - 50 IS - 4 SP - 447 EP - 461 ER - TY - GEN A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 -- a Flexible Finite Element Toolbox N2 - Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the Dune interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way. T3 - ZIB-Report - 19-48 KW - finite elements KW - generic programming KW - partial differential equations Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-74616 SN - 1438-0064 ER -