# Domain decomposition and matrix free methods

**URL:** <https://community.freefem.org/t/domain-decomposition-and-matrix-free-methods/156>\
**Category:** General Discussion\
**Created:** [October 17, 2019, 4:58pm UTC](https://community.freefem.org/t/domain-decomposition-and-matrix-free-methods/156 "2019-10-17T16:58:45Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![miguel](https://avatars.discourse-cdn.com/v4/letter/m/439d5e/32.png) [@miguel](https://community.freefem.org/u/miguel)\
**Post date:** [October 17, 2019, 4:58pm UTC](https://community.freefem.org/t/domain-decomposition-and-matrix-free-methods/156/1 "2019-10-17T16:58:45Z")

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Can domain decomposition methods be used without having to assemble the operator? My concern is that there is a trend towards matrix free methods for very large scale problems. I wonder how domain decomposition deal with this. I am new to DD methods, I would appreciate if anybody could point me to a paper with such implementation or if it is possible on FreeFEM++

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**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\
**Post date:** [October 20, 2019, 3:28pm UTC](https://community.freefem.org/t/domain-decomposition-and-matrix-free-methods/156/2 "2019-10-20T15:28:34Z")

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Yes, it’s possible. You just need to define your matrix–vector product and supply a preconditioner. Then, either PETSc or HPDDM will solve the problem using your Krylov method of choice. Here, have a look at this [example](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/iterative.edp).