Add contribution section

doc/expose/expose.tex

@@ -64,6 +64,7 @@ From an implementor's perspective, the \acrshort{cpm} has a great advantage over
 Since updates happen on a square lattice and changes in energy can be calculated locally, it lends itself well to distributed programming.
 \acrfull{cis}~\cite{berghoff2020} is a parallel implementation of the \acrshort{cpm} based on the \acrfull{nastja} framework~\cite{berghoff2018}.
 \acrshort{nastja} offers an abstraction layer for implementing stencil codes on the \acrfull{mpi}, making it possible to leverage large-scale parallelism for \acrshort{cis}.
+\acrshort{nastja} divides the domain into blocks, computing each stencil locally, then performing an halo exchanges of the border regions.
 
 \subsection{The \acrfull{ecm}}
 
@@ -86,7 +87,7 @@ We focus on approaches that explicitly model the plasticity of \acrshort{ecm} co
 
 A starting point is to model the \acrshort{ecm} as a static cell.
 In this model, a cell ID is chosen to represent the solid parts of the \acrshort{ecm}.
-Cell-matrix interactions are regulated by the hamiltonian just like cell-cell interactions.
+Cell-matrix interactions are regulated by the Hamiltonian just like cell-cell interactions.
 \acrshort{ecm} lattice sites do not copy their neighbors and can not be copied by their neighbors during a \acrshort{mcs}.
 Instead, simulations using this approach usually allow cells to degrade adjacent matrix sites over time.
 This approach is used for example in~\cite{bauer2007}, where the \acrshort{ecm} is initialized by randomly placing fiber bundles across the domain and~\cite{scianna2013}, which investigates cell behavior in \acrshortpl{ecm} with regular patterns.
@@ -95,13 +96,13 @@ This approach is used for example in~\cite{bauer2007}, where the \acrshort{ecm}
 
 An approach using a \acrfull{fem} is presented in~\cite{vanoers2014} and expanded upon in~\cite{rens2017, rens2019}.
 Each lattice site is assigned a local directional strain on the \acrshort{ecm}.
-Cells exert a traction forces on the \acrshort{ecm} used to calculate the lattice strains by a \acrshort{fem}.
+Cells exert traction forces on the \acrshort{ecm} used to calculate the lattice strains by a \acrshort{fem}.
 The hamiltonian of the \acrshort{cpm} is modified such that cells respond to the strain.
 
 \paragraph{Hybrid \acrshort{cpm} and Molecular Dynamics Methods}
 
 Another approach is presented in~\cite{tsingos2022}.
-This work models simulates matrix fibers using a bead-and-chain model.
+This work simulates matrix fibers using a bead-and-chain model.
 Similar to the previous approach, the \acrshort{ecm} model is coupled with the \acrshort{cpm}.
 However, in this work, cells interact with the \acrshort{ecm} only through a sparse subset of lattice sites.
 
@@ -125,24 +126,56 @@ In order to align the viscoelastic \acrshort{ecm} model with the \acrshort{cpm},
 
 A model for viscoelastic solids is presented in~\cite{obrien2008}.
 This work extends the discrete particle method for elastic solids presented in~\cite{toomey2000}.
-This model is based on a two- or three-dimensional square lattice of particles.
+It is based on a two- or three-dimensional square lattice of particles.
-Each particle is connected to all of its Moore neighbors.
+Each particle is connected to all of its cardinal and diagonal neighbors.
 The model for the force acting between two particles can be elastic or viscoelastic.
 Various models are explored in~\cite{obrien2008, obrien2009, obrien2014, obrien2021}.
 
 \paragraph{\acrfull{lbm}}
 
-The \acrshort{lbm} is an established approach for modeling the dynamics of fluids.~\cite{krueger2017}
+The \acrshort{lbm} is an established approach for modeling the dynamics of fluids~\cite{krueger2017}.
 Also based on a square lattice, this model discretizes the particles moving at a particular lattice space into the cardinal and diagonal directions.
 Research suggests that the \acrshort{lbm} can be used for modeling both solids~\cite{maquart2022} and viscoelastic fluids~\cite{malaspinas2010}.
 Perhaps for this particular use case, a \acrshort{lbm} could be configured to model the \acrshort{ecm}.
 
 \section{Contribution}
 
+In this work we will explore lattice-based viscoelastic simulations of the \acrshort{ecm} in the \acrshort{cpm}.
+
 \subsection{Method}
 
+For the \acrshort{cpm} we use the distributed implementation \acrshort{cis}.
+\acrshort{cis} is based on the \acrshort{nastja} framework implemented using the \acrshort{mpi}, which we will use to develop our model of the \acrshort{ecm}.
+The model will likely be based on the viscoelastic discrete particle method, as preliminary experiments based on a simplified implementation show promising results.
+
+In order to model cell-matrix interactions, we will develop a method that allows cells to influence the \acrshort{ecm} simulation.
+To model matrix-cell interactions, we will expand the Hamiltonian of the \acrshort{cpm} to include a term dependent on the local configuration of the \acrshort{ecm}.
+This should make it possible for our model to simulate the self-reinforcing interactions of cells and \acrshort{ecm}.
+
 \subsection{Challenges}
 
+Our preliminary experiments have produced some questions and likely challenges that our work will need to address.
+
+\paragraph{Spatial Scale}
+
+While we could simply use the same lattice for the \acrshort{ecm} model as for the \acrshort{cpm}, it is not clear that this will deliver the best results.
+It could be useful to use a scaled lattice, e.g.\ where the lattice spacing of the \acrshort{ecm} model is twice as long.
+
+\paragraph{Temporal Scale}
+
+Compared to cells, the waves in a viscoelastic material move quickly.
+It is likely that our model of the \acrshort{ecm} will have to go through multiple time steps between the \acrshortpl{mcs} of the \acrshort{cpm}.
+In the context of \acrshort{nastja}, this means an increased number of halo exchanges between ranks per \acrshort{mcs}.
+In order to reduce the number of halo exchanges, we could increase the width of the halo which allows the \acrshort{ecm} simulation to run for multiple time steps between halo exchanges.
+As this approach necessarily leads to diminishing returns as the halo data gets bigger, an efficient configuration needs to be investigated.
+
+\paragraph{Implementation Performance}
+
+As \acrshort{cis} is designed to large and therefore compute-heavy simulations, it is worthwhile to measure the and optimize the compute needed by our implementation.
+Since the discrete particle method is a dense approach, it should be possible to leverage common parallelization techniques such as vectorization and \acrshort{gpu} programming to improve performance.
+In particular, it might prove useful to run the \acrshort{cpm} on \acrshortpl{cpu} and the \acrshort{ecm} model of \acrshortpl{gpu}.
+We will experiment with these techniques and evaluate the possible improvements.
+
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