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<span style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 10pt; color: rgb(0, 0, 0);">Dear PETSc Users, </span></div>
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<span style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 10pt;"></span><span style="font-size: 10pt; color: rgb(0, 0, 0); font-family: Calibri, Arial, Helvetica, sans-serif;">As a part of my problem, I need to be able to look up the value
of a scalar field (let's call it xi) that is defined via a somewhat non-trivial integral over a second scalar field (let's call it rho). Mathematically we have</span></div>
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<span style="font-size: 10pt; color: rgb(0, 0, 0);"> </span><img size="6066" contenttype="image/png" id="img972631" aria-expanded="false" tabindex="0" style="font-size: 10pt; color: rgb(33, 33, 33); max-width: 99.9%; -webkit-user-select: none;" src="cid:07284a17-07f8-426b-85da-461ebc1fe4b8"></div>
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<span style="font-size: 10pt;">What we're modeling here is the average energy loss of an energetic ion that is passing through a solid material. Ions can arrive with a specified direction, so to calculate xi at each point, we have to perform line integrals
back toward the ion source, and keep track of how much mass the ion has passed through.</span><br>
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<span style="font-size: 10pt; color: rgb(33, 33, 33);"></span><span style="font-size: 10pt; color: rgb(0, 0, 0);">In a serial algorithm, one can in principle generate xi by working from the top down, subtracting energy from each row of grid points given information
on the density field. However, it is not clear how one could develop a robust parallel algorithm, much less one that works within the PETSc framework.</span></div>
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<span style="font-size: 10pt; color: rgb(33, 33, 33);"></span><span style="color: rgb(0, 0, 0); font-size: 10pt;">I would very grateful for any help you can offer.</span><span style="font-size: 10pt;"></span></div>
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<span style="font-size: 10pt; color: rgb(0, 0, 0);">Sincerely,</span></div>
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<span style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 10pt; color: rgb(0, 0, 0);">Jennifer Swenson</span></div>
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