<liclass="toctree-l4"><aclass="reference internal"href="#constructing-a-mesh-for-the-sn-calculation">Constructing a mesh for the S<sub>N</sub> calculation</a></li>

<liclass="toctree-l4"><aclass="reference internal"href="#macromaterials-for-sn-geometries">Macromaterials for S<sub>N</sub> geometries</a></li>

<spanid="mavric"></span><h1>MAVRIC: Monaco with Automated Variance Reduction using Importance Calculations<aclass="headerlink"href="#mavric-monaco-with-automated-variance-reduction-using-importance-calculations"title="Permalink to this headline">¶</a></h1>

<p><em>D. E. Peplow and C. Celik</em></p>

<divclass="section"id="introduction">

<h2>Introduction<aclass="headerlink"href="#introduction"title="Permalink to this headline">¶</a></h2>

<p>Monte Carlo particle transport calculations for deep penetration problems can require very long run times in order to achieve an acceptable level of statistical uncertainty in the final answers. Discrete-ordinates codes can be faster but have limitations relative to the discretization of space, energy, and direction. Monte Carlo calculations can be modified (biased) to produce results with the same variance in less time if an approximate answer or some other additional information is already known about the problem. If an importance can be assigned to different particles based on how much they will contribute to the final answer, more time can be spent on important particles with less time devoted to unimportant particles. One of the best ways to bias a Monte Carlo code for a particular tally is to form an importance map from the adjoint flux based on that tally. Unfortunately, determining the exact adjoint flux could be just as difficult as computing the original problem itself. However, an approximate adjoint can still be very useful in biasing the Monte Carlo solution <aclass="bibtex reference internal"href="#wagner-acceleration-1997"id="id1">[Wag97]</a>. Discrete ordinates can be used to quickly compute that approximate adjoint. Together, Monte Carlo and discrete ordinates can be used to find solutions to thick shielding problems in reasonable times.</p>

<p>The MAVRIC (Monaco with Automated Variance Reduction using Importance Calculations) sequence is based on the CADIS (Consistent Adjoint Driven Importance Sampling) and FW-CADIS (Forward-Weighted CADIS) methodologies <aclass="bibtex reference internal"href="#wagner-automated-1998"id="id2">[WH98]</a><aclass="bibtex reference internal"href="#wagner-automated-2002"id="id3">[Wag02]</a><aclass="bibtex reference internal"href="#haghighat-monte-2003"id="id4">[HW03]</a><aclass="bibtex reference internal"href="#wagner-forward-weighted-2007"id="id5">[WBP07]</a> MAVRIC automatically performs a three-dimensional, discrete-ordinates calculation using Denovo to compute the adjoint flux as a function of position and energy. This adjoint flux information is then used to construct an importance map (i.e., target weights for weight windows) and a biased source distribution that work together—particles are born with a weight matching the target weight of the cell into which they are born. The fixed-source Monte Carlo radiation transport Monaco then uses the importance map for biasing during particle transport and the biased source distribution as its source. During transport, the particle weight is compared with the importance map after each particle interaction and whenever a particle crosses into a new importance cell in the map.</p>

<p>For problems that do not require variance reduction to complete in a reasonable time, execution of MAVRIC without the importance map calculation provides an easy way to run Monaco. For problems that do require variance reduction to complete in a reasonable time, MAVRIC removes the burden of setting weight windows from the user and performs it automatically with a minimal amount of additional input. Note that the MAVRIC sequence can be used with the final Monaco calculation as either a multigroup (MG) or a continuous-energy (CE) calculation.</p>

<p>Monaco has a wide variety of tally options: it can calculate fluxes (by group) at a point in space, over any geometrical region, or for a user-defined, three-dimensional, rectangular grid. These tallies can also integrate the fluxes with either standard response functions from the cross section library or user-defined response functions. All of these tallies are available in the MAVRIC sequence.</p>

<p>While originally designed for CADIS, the MAVRIC sequence is also capable of creating importance maps using both forward and adjoint deterministic estimates. The FW-CADIS method can be used for optimizing several tallies at once, a mesh tally over a large region, or a mesh tally over the entire problem. Several other methods for producing importance maps are also available in MAVRIC and are explored in Appendix C.</p>

</div>

<divclass="section"id="cadis-methodology">

<h2>CADIS Methodology<aclass="headerlink"href="#cadis-methodology"title="Permalink to this headline">¶</a></h2>

<p>MAVRIC is an implementation of CADIS (Consistent Adjoint Driven Importance Sampling) using the Denovo SN and Monaco Monte Carlo functional modules. Source biasing and a mesh-based importance map, overlaying the physical geometry, are the basic methods of variance reduction. In order to make the best use of an importance map, the map must be made consistent with the source biasing. If the source biasing is inconsistent with the weight windows that will be used during the transport process, source particles will undergo Russian roulette or splitting immediately, wasting computational time and negating the intent of the biasing.</p>

<divclass="section"id="overview-of-cadis">

<h3>Overview of CADIS<aclass="headerlink"href="#overview-of-cadis"title="Permalink to this headline">¶</a></h3>

<p>CADIS has been well described in the literature, so only a

brief overview is given here. Consider a class source-detector problem

described by a unit source with emission probability distribution

function <spanclass="math notranslate nohighlight">\(q\left(\overrightarrow{r},E \right)\)</span> and a detector

response function <spanclass="math notranslate nohighlight">\(\sigma_{d}\left(\overrightarrow{r},E \right)\)</span>.

To determine the total detector response, <em>R</em>, the forward scalar flux

<spanclass="math notranslate nohighlight">\(\phi\left(\overrightarrow{r},E \right)\)</span> must be known. The

response is found by integrating the product of the detector response

function and the flux over the detector volume <spanclass="math notranslate nohighlight">\(V_{d}\)</span>.</p>

<spanclass="eqno">(1)<aclass="headerlink"href="#equation-mavric-1"title="Permalink to this equation">¶</a></span>\[R = \int_{V_{d}}^{}{\int_{E}^{}{\sigma_{d}\left( \overrightarrow{r},E \right)}}\phi\left(\overrightarrow{r},E \right)\textit{dE dV.}\]</div>

<p>Alternatively, if the adjoint scalar flux,

<spanclass="math notranslate nohighlight">\(\phi^{+}\left(\overrightarrow{r},E \right)\)</span>, is known from the

<spanclass="eqno">(2)<aclass="headerlink"href="#equation-mavric-2"title="Permalink to this equation">¶</a></span>\[R = \int_{V_{s}}^{}{\int_{E}^{}{q\left(\overrightarrow{r},E \right)}}\phi^{+}\left( \overrightarrow{r},E \right)\textit{dE dV.}\]</div>

<p>Unfortunately, the exact adjoint flux may be just as difficult to

determine as the forward flux, but an approximation of the adjoint flux

can still be used to form an importance map and a biased source

distribution for use in the forward Monte Carlo calculation.</p>

<p>Wagner<sup>1</sup> showed that if an estimate of the adjoint scalar flux

for the corresponding adjoint problem could be found, then an estimate

of the response <em>R</em> could be made using Eq. . The adjoint source for the

adjoint problem is typically separable and corresponds to the detector

response and spatial area of tally to be optimized:

<spanclass="eqno">(3)<aclass="headerlink"href="#equation-mavric-3"title="Permalink to this equation">¶</a></span>\[\widehat{q}\left(\overrightarrow{r},E \right) = \frac{1}{R}q\left(\overrightarrow{r},E\right)\phi^{+}\left( \overrightarrow{r},E \right)\]</div>

<p>and weight window target values,

<spanclass="math notranslate nohighlight">\(\overline{w}\left( \overrightarrow{r},E \right)\)</span>, for particle

<spanclass="eqno">(4)<aclass="headerlink"href="#equation-mavric-4"title="Permalink to this equation">¶</a></span>\[\overline{w}\left( \overrightarrow{r},E \right) = \frac{R}{\phi^{+}\left( \overrightarrow{r},E \right)}\]</div>

<p>could be constructed, which minimize the variance in the forward Monte

Carlo calculation of <em>R</em>.</p>

<p>When a particle is sampled from the biased source distribution

<spanclass="math notranslate nohighlight">\(\widehat{q}\left( \overrightarrow{r},E \right)\)</span>, to preserve a

<spanclass="eqno">(6)<aclass="headerlink"href="#equation-mavric-6"title="Permalink to this equation">¶</a></span>\[w_{0} \equiv \ \left(\frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left(\frac{q_{i}\left( \overrightarrow{r},E \right)}{{\widehat{q}}_{i}\left( \overrightarrow{r},E \right)} \right)\text{.}\]</div>

<p>For CADIS, a biased multiple source needs to be developed so that the

birth weights of sampled particles still match the target weights of the

importance map. For a problem with multiple sources (each with a

distribution <spanclass="math notranslate nohighlight">\(q_{i}\left( \overrightarrow{r},E \right)\)</span> and a

strength <spanclass="math notranslate nohighlight">\(S_{i}\)</span>), the goal of the Monte Carlo calculation is to

compute some response <spanclass="math notranslate nohighlight">\(R\)</span> for a response function

<spanclass="math notranslate nohighlight">\(\sigma_{d}\left( \overrightarrow{r},E \right)\)</span> at a given

<spanclass="eqno">(8)<aclass="headerlink"href="#equation-mavric-8"title="Permalink to this equation">¶</a></span>\[R_{i} = \ \int_{V}^{}{\int_{E}^{}{\sigma_{d}\left(\overrightarrow{r},E \right)\ \phi_{i}\left(\overrightarrow{r},E \right)\textit{dE dV .}}}\]</div>

<p>The total response is then found as <spanclass="math notranslate nohighlight">\(R = \sum_{i}^{}R_{i}\)</span>.</p>

<p>For the adjoint problem, using the adjoint source of

<spanclass="eqno">(10)<aclass="headerlink"href="#equation-mavric-10"title="Permalink to this equation">¶</a></span>\[R_{i} = \ \int_{V}^{}{\int_{E}^{}{\ {S_{i}q_{i}\left( \overrightarrow{r},E \right)\text{ϕ}}^{+}\left( \overrightarrow{r}, E \right)\textit{dE dV.}}}\]</div>

<p>The target weights

<spanclass="math notranslate nohighlight">\(\overline{w}\left( \overrightarrow{r},E \right)\)</span> of the

<spanclass="eqno">(12)<aclass="headerlink"href="#equation-mavric-12"title="Permalink to this equation">¶</a></span>\[{\widehat{q}}_{i}\left(\overrightarrow{r},E \right) = \frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\text{ϕ}}^{+}\left( \overrightarrow{r}, E \right)\ ,\]</div>

<p>and the biased distribution used to select an individual source is

<spanclass="math notranslate nohighlight">\(\widehat{p}\left( i \right) = \ R_{i}/\sum_{}^{}{R_{i} = R_{i}/R}\)</span>.</p>

<p>When using the biased distribution used to select an individual source,

<spanclass="math notranslate nohighlight">\(\widehat{p}\left( i \right)\)</span>, and the biased source distribution,

<spanclass="math notranslate nohighlight">\({\widehat{q}}_{i}\left( \overrightarrow{r},E \right)\)</span>, the birth

<spanclass="eqno">(13)<aclass="headerlink"href="#equation-mavric-13"title="Permalink to this equation">¶</a></span>\[\begin{split} \begin{matrix}

w_{0} & \equiv & \left( \frac{p\left( i \right)}{\widehat{p}\left( i \right)} \right)\left( \frac{q_{i}\left( \overrightarrow{r}, E \right)}{{\widehat{q}}_{i}\left(\overrightarrow{r},E \right)} \right) \\ & = & \ \left( \frac{\frac{S_{i}}{S}}{\frac{R_{i}}{R}} \right) \left( \frac{q_{i}\left( \overrightarrow{r},E \right)}{\frac{S_{i}}{R_{i}}{q_{i}\left( \overrightarrow{r},E \right)\text{ϕ}}^{+}\left( \overrightarrow{r},E \right)} \right) \\

& = & \frac{R/S}{\text{ϕ}^{+}\left( \overrightarrow{r},E \right)\ }, \\

<h3>Multiple tallies with CADIS<aclass="headerlink"href="#multiple-tallies-with-cadis"title="Permalink to this headline">¶</a></h3>

<p>The CADIS methodology works quite well for classic source/detector problems. The statistical uncertainty of the tally that serves as the adjoint source is greatly reduced since the Monte Carlo transport is optimized to spend more simulation time on those particles that contribute to the tally, at the expense of tracking particles in other parts of phase space. However, more recently, Monte Carlo has been applied to problems where multiple tallies need to all be found with low statistical uncertainties. The extension of this idea is the mesh tally—where each voxel is a tally where the user desires low statistical uncertainties. For these problems, the user must accept a total simulation time that is controlled by the tally with the slowest convergence and simulation results where the tallies have a wide range of relative uncertainties.</p>

<p>The obvious way around this problem is to create a separate problem for each tally and use CADIS to optimize each. Each simulation can then be run until the tally reaches the level of acceptable uncertainty. For more than a few tallies, this approach becomes complicated and time-consuming for the user. For large mesh tallies, this approach is not reasonable.</p>

<p>Another approach to treat several tallies, if they are in close proximity to each other, or a mesh tally covering a small portion of the physical problem is to use the CADIS methodology with the adjoint source near the middle of the tallies to be optimized. Since particles in the forward Monte Carlo simulation are optimized to reach the location of the adjoint source, all the tallies surrounding that adjoint source should converge quickly. The drawback to this approach is the difficult question of “how close.” If the tallies are too far apart, certain energies or regions that are needed for one tally may be of low importance for getting particles to the central adjoint source. This may under-predict the flux or dose at the tally sites far from the adjoint source.</p>

<p>MAVRIC has the capability to have multiple adjoint sources with this problem in mind. For several tallies that are far from each other, multiple adjoint sources could be used. In the forward Monte Carlo, particles would be drawn to one of those adjoint sources. The difficulty with this approach is that typically the tally that is closest to the true physical source converges faster than the other tallies—showing the closest adjoint source seems to attract more particles than the others. Assigning more strength to the adjoint source further from the true physical source helps, but finding the correct strengths so that all of the tallies converge to the same relative uncertainty in one simulation is an iterative process for the user.</p>

</div>

<divclass="section"id="forward-weighted-cadis">

<h3>Forward-weighted CADIS<aclass="headerlink"href="#forward-weighted-cadis"title="Permalink to this headline">¶</a></h3>

<p>In order to converge several tallies to the same relative uncertainty in

one simulation, the adjoint source corresponding to each of those

tallies needs to be weighted inversely by the expected tally value. In

order to calculate the dose rate at two points—say one near a reactor

and one far from a reactor—in one simulation, then the total adjoint

source used to develop the weight windows and biased source needs to

have two parts. The adjoint source far from the reactor needs to have

more strength than the adjoint source near the reactor by a factor equal

to the ratio of the expected near dose rate to the expected far dose

rate.</p>

<p>This concept can be extended to mesh tallies as well. Instead of using a

uniform adjoint source strength over the entire mesh tally volume, each

voxel of the adjoint source should be weighted inversely by the expected

forward tally value for that voxel. Areas of low flux or low dose rate

would have more adjoint source strength than areas of high flux or high

dose rate.</p>

<p>An estimate of the expected tally results can be found by using a quick

discrete-ordinates calculation. This leads to an extension of the CADIS

method: forward-weighted CADIS (FW-CADIS).**Error! Bookmark not

defined.** First, a forward S<sub>N</sub> calculation is performed to

estimate the expected tally results. A total adjoint source is

constructed where the adjoint source corresponding to each tally is

weighted inversely by those forward tally estimates. Then the standard

CADIS approach is used—an importance map (target weight windows) and a

biased source are made using the adjoint flux computed from the adjoint

S<sub>N</sub> calculation.</p>

<p>For example, if the goal is to calculate a detector response function

<spanclass="math notranslate nohighlight">\(\sigma_{d}\left( E \right)\)</span> (such as dose rate using

flux-to-dose-rate conversion factors) over a volume (defined by

<spanclass="math notranslate nohighlight">\(g\left( \overrightarrow{r} \right)\)</span>) corresponding to mesh tally,

then instead of simply using

<spanclass="math notranslate nohighlight">\(q^{+}\left( \overrightarrow{r},E \right) = \sigma_{d}\left( E \right)\ g(\overrightarrow{r})\)</span>,

<spanclass="eqno">(14)<aclass="headerlink"href="#equation-mavric-14"title="Permalink to this equation">¶</a></span>\[ q^{+}\left( \overrightarrow{r},E \right) = \frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\text{ϕ}\left( \overrightarrow{r},E \right)}\textit{dE}}\ ,\]</div>

<p>where <spanclass="math notranslate nohighlight">\(\phi\left( \overrightarrow{r},E \right)\)</span> is an estimate of

the forward flux and the energy integral is over the voxel at <spanclass="math notranslate nohighlight">\(\overrightarrow{r}\)</span>.

The adjoint source is nonzero only where the mesh tally is defined

(<spanclass="math notranslate nohighlight">\(g\left( \overrightarrow{r} \right)\)</span>), and its strength is

inversely proportional to the forward estimate of dose rate.</p>

<p>The relative uncertainty of a tally is controlled by two components:

first, the number of tracks contributing to the tally and, second, the

shape of the distribution of scores contributing to that tally. In the

Monte Carlo game, the number of simulated particles,

<spanclass="math notranslate nohighlight">\(m\left( \overrightarrow{r},E \right)\)</span>, can be related to the true

<trclass="row-even"><td><p>Spatially dependent total response. <spanclass="math notranslate nohighlight">\(\int_{}^{}{\sigma_{d}\left( E \right)\text{ϕ}\left(\overrightarrow{r},E\right)}\textit{dE}\)</span></p></td>

<td><divclass="math notranslate nohighlight">

\[\frac{\sigma_{d}\left( E \right)\text{g}\left( \overrightarrow{r} \right)}{\int_{}^{}{\sigma_{d}\left( E \right)\text{ϕ}\left( \overrightarrow{r},E \right)}\textit{dE}}\]</div>

</td>

</tr>

</tbody>

</table>

<p>The bottom line of FW-CADIS is that in order to calculate a quantity at

multiple tally locations (or across a mesh tally) with more uniform

relative uncertainties, an adjoint source needs to be developed for an

objective function that keeps some non-physical quantity—related to the

Monte Carlo particle density and similar in form to the desired

quantity—constant. FW-CADIS uses the solution of a forward

discrete-ordinates calculation to properly weight the adjoint source.

After that, the standard CADIS approach is used.</p>

<h2>MAVRIC Implementation of CADIS<aclass="headerlink"href="#mavric-implementation-of-cadis"title="Permalink to this headline">¶</a></h2>

<p>With MAVRIC, as with other shielding codes, the user defines the problem as a set of physical models—the material compositions, the geometry, the source, and the detectors (locations and response functions)—as well as some mathematical parameters on how to solve the problem (number of histories, etc.). For the variance reduction portion of MAVRIC, the only additional inputs required are (1) the mesh planes to use in the discrete-ordinates calculation(s) and (2) the adjoint source description—basically the location and the response of each tally to optimize in the forward Monte Carlo calculation. MAVRIC takes this information and constructs a Denovo adjoint problem. (The adjoint source is weighted by a Denovo forward flux or response estimate for FW-CADIS applications.) MAVRIC then uses the CADIS methodology: it combines the adjoint flux from the Denovo calculation with the source description and creates the importance map (weight window targets) and the mesh-based biased source. Monaco is then run using the CADIS biased source distribution and the weight window targets.</p>

<divclass="section"id="denovo">

<h3>Denovo<aclass="headerlink"href="#denovo"title="Permalink to this headline">¶</a></h3>

<p>Denovo is a parallel three-dimensional SN code that is used to generate adjoint (and, for FW-CADIS, forward) scalar fluxes for the CADIS methods in MAVRIC. For use in MAVRIC/CADIS, it is highly desirable that the SN code be fast, positive, and robust. The phase-space shape of the forward and adjoint fluxes, as opposed to a highly accurate solution, is the most important quality for Monte Carlo weight-window generation. Accordingly, Denovo provides a step-characteristics spatial differencing option that produces positive scalar fluxes as long as the source (volume plus in-scatter) is positive. Denovo uses an orthogonal, nonuniform mesh that is ideal for CADIS applications because of the speed and robustness of calculations on this mesh type.</p>

<p>Denovo uses the highly robust GMRES (Generalized Minimum Residual) Krylov method to solve the SN equations in each group. GMRES has been shown to be more robust and efficient than traditional source (fixed-point) iteration. The in-group discrete SN equations are defined as</p>

<spanclass="eqno">(16)<aclass="headerlink"href="#equation-mavric-16"title="Permalink to this equation">¶</a></span>\[\mathbf{L}\psi = \mathbf{\text{MS}}\phi + q\]</div>

<p>where <strong>L</strong> is the differential transport operator, <strong>M</strong> is the

moment-to-discrete operator, <strong>S</strong> is the matrix of scattering

cross-section moments, <em>q</em> is the external and in-scatter source,

<spanclass="math notranslate nohighlight">\(\phi\)</span> is the vector of angular flux moments, and <spanclass="math notranslate nohighlight">\(\psi\)</span> is

the vector of angular fluxes at discrete angles. Applying the operator

<strong>D</strong>, where <spanclass="math notranslate nohighlight">\(\phi = \mathbf{D}\psi\)</span>, and rearranging terms casts

the in-group equations in the form of a traditional linear system,

<spanclass="eqno">(17)<aclass="headerlink"href="#equation-mavric-17"title="Permalink to this equation">¶</a></span>\[\left( \mathbf{I} - \mathbf{D}\mathbf{L}^{- 1}\mathbf{\text{MS}} \right) = \mathbf{D}\mathbf{L}^{- 1}q .\]</div>

</div></blockquote>

<p>The operation <spanclass="math notranslate nohighlight">\(\mathbf{L}^{- 1}\nu\)</span>, where <spanclass="math notranslate nohighlight">\(\nu\)</span> is an

iteration vector, is performed using a traditional wave-front solve

(transport sweep). The parallel implementation of the Denovo wave-front

solver uses the well-known Koch-Baker-Alcouffe (KBA) algorithm, which is

a two-dimensional block‑spatial decomposition of a three-dimensional

orthogonal mesh <aclass="bibtex reference internal"href="#baker-sn-1998"id="id6">[BK98]</a>. The Trilinos package is used for the GMRES

implementation <aclass="bibtex reference internal"href="#willenbring-trilinos-2003"id="id7">[WH03]</a> Denovo stores the mesh-based scalar fluxes in a

double precision binary file (<ahref="#id8"><spanclass="problematic"id="id9">*</span></a>.dff) called a Denovo flux file. Past

versions of SCALE/Denovo used the TORT <aclass="bibtex reference internal"href="#rhoades-tort-1997"id="id10">[RS97]</a> *.varscl file format

(DOORS package <aclass="bibtex reference internal"href="#rhoades-doors-1998"id="id11">[RC98]</a>), but this was limited to single precision. Since

the rest of the MAVRIC sequence has not yet been parallelized, Denovo is

currently used only in serial mode within MAVRIC.</p>

</div>

<divclass="section"id="monaco">

<h3>Monaco<aclass="headerlink"href="#monaco"title="Permalink to this headline">¶</a></h3>

<p>The forward Monte Carlo transport is performed using Monaco, a

fixed-source, shielding code that uses the SCALE General Geometry

Package (SGGP, the same as used by the criticality code KENO-VI) and the

standard SCALE material information processor. Monaco can use either MG

or CE cross section libraries. Monaco was originally based on the MORSE

Monte Carlo code but has been extensively modified to modernize the

coding, incorporate more flexibility in terms of sources/tallies, and

read a user-friendly block/keyword style input.</p>

<p>Much of the input to MAVRIC is the same as Monaco. More details can be

found in the Monaco chapter of the SCALE manual.</p>

</div>

<divclass="section"id="running-mavric">

<h3>Running MAVRIC<aclass="headerlink"href="#running-mavric"title="Permalink to this headline">¶</a></h3>

<p>The objective of a SCALE sequence is to execute several codes, passing

the output from one to the input of the next, in order to perform some

analysis—things that users typically had to do in the past. MAVRIC does

this for difficult shielding problems by running approximate

discrete-ordinates calculations, constructing an importance map and

biased source for one or more tallies that the user wants to optimize in

the Monte Carlo calculation, and then using those in a forward Monaco

Monte Carlo calculation. MAVRIC also prepares the forward and adjoint

cross sections when needed. The steps of a MAVRIC sequence are listed in

<aclass="reference internal"href="#mavric-sequence"><spanclass="std std-numref">Table 1</span></a>. The user can instruct MAVRIC to run this whole sequence of

steps or just some subset of the steps—in order to verify the

intermediate steps or to reuse previously calculated quantities in a new

analyses.</p>

<p>The MAVRIC sequence can be stopped after key points by using the

“parm= <em>parameter</em> ” operator on the “=mavric” command line, which is

the first line of the input file. The various parameters are listed in

Table <aclass="reference internal"href="#mavric-param"><spanclass="std std-numref">Table 2</span></a>. These parameters allow the user to perform checks and make

changes to the importance map calculation before the actual Monte Carlo

calculation in Monaco.</p>

<p>MAVRIC also allows the sequence to start at several different points. If

an importance map and biased source have already been computed, they can

be used directly. If the adjoint scalar fluxes are known, they can

quickly be used to create the importance map and biased source and then

begin the forward Monte Carlo. All of the different combinations of

starting MAVRIC with some previously calculated quantities are listed in

the following section detailing the input options.</p>

<p>When using MG cross-section libraries that do not have flux-to-dose-rate

conversion factors, use “parm=nodose” to prevent the cross section

processing codes from trying to move these values into the working

library.</p>

<p>MAVRIC creates many files that use the base problem name from the output

file. For an output file called “c:path1path2\<em>outputName</em>.out” or

“/home/path1/path2/ <em>outputName</em>.inp”, spaces in the output name will

<caption><spanclass="caption-number">Table 1 </span><spanclass="caption-text">Steps in the MAVRIC sequence</span><aclass="headerlink"href="#mavric-sequence"title="Permalink to this table">¶</a></caption>

<caption><spanclass="caption-number">Table 2 </span><spanclass="caption-text">Parameters for the MAVRIC command line (“parm=…”)</span><aclass="headerlink"href="#mavric-param"title="Permalink to this table">¶</a></caption>

<thclass="head"><p>MAVRIC will stop after</p></th>

</tr>

</thead>

<tbody>

<trclass="row-even"><td><p>check</p></td>

<td><p>input checking</p></td>

</tr>

<trclass="row-odd"><td><p>forinp</p></td>

<td><p>Forward Denovo input construction (makes <codeclass="docutils literal notranslate"><spanclass="pre">xkba_b.inp</span></code> in the tmp area)</p></td>

</tr>

<trclass="row-even"><td><p>forward</p></td>

<td><p>The forward Denovo calculation</p></td>

</tr>

<trclass="row-odd"><td><p>adjinp</p></td>

<td><p>Adjoint Denovo input construction (makes <codeclass="docutils literal notranslate"&