Adding AD version of MatchedValueBC

Closes idaholab#18212

framework/doc/content/source/bcs/ADMatchedValueBC.md

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+# ADMatchedValueBC
+
+!syntax description /BCs/ADMatchedValueBC
+
+## Description
+
+`ADMatchedValueBC` is a `ADNodalBC` which applies to systems of two or more variables,
+and can be used to impose equality of two solutions along a given `boundary`.
+This class is appropriate for systems of partial differential equations (PDEs) of
+the form
+\begin{equation}
+\begin{aligned}
+  -\nabla^2 u &= f_1 && \quad \in \Omega \\
+  -\nabla^2 v &= f_2 && \quad \in \Omega \\
+  \frac{\partial u}{\partial n} &= h_1 && \quad \in \partial \Omega_N \\
+  \frac{\partial v}{\partial n} &= h_2 && \quad \in \partial \Omega_N \\
+  u &= v && \quad \in \partial \Omega_D,
+\end{aligned}
+\end{equation}
+where $\Omega \subset \mathbb{R}^n$ is the domain, and $\partial
+\Omega = \partial \Omega_D \cup \partial \Omega_N$ is its boundary,
+$u$, $v$ are the unknowns, $f_1$, $f_2$ are forcing functions (which
+may depend on both $u$ and $v$), and $h_1$ and $h_2$ are given
+fluxes. The `v` parameter is used to specify the variable whose value
+is tied to $u$. In the example below, the other variable's name
+happens to be `v` as well.
+
+## Example Input Syntax
+
+!listing test/tests/bcs/ad_matched_value_bc/test.i start=[left_u] end=[] include-end=true
+
+!syntax parameters /BCs/ADMatchedValueBC
+
+!syntax inputs /BCs/ADMatchedValueBC
+
+!syntax children /BCs/ADMatchedValueBC

framework/include/bcs/ADMatchedValueBC.h

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+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#pragma once
+
+#include "ADNodalBC.h"
+
+/**
+ * Implements a simple coupled boundary condition where u=v on the boundary.
+ */
+class ADMatchedValueBC : public ADNodalBC
+{
+public:
+  static InputParameters validParams();
+
+  ADMatchedValueBC(const InputParameters & parameters);
+
+protected:
+  virtual ADReal computeQpResidual() override;
+
+  const ADVariableValue & _v;
+};

framework/src/bcs/ADMatchedValueBC.C

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+//* This file is part of the MOOSE framework
+//* https://www.mooseframework.org
+//*
+//* All rights reserved, see COPYRIGHT for full restrictions
+//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
+//*
+//* Licensed under LGPL 2.1, please see LICENSE for details
+//* https://www.gnu.org/licenses/lgpl-2.1.html
+
+#include "ADMatchedValueBC.h"
+
+registerMooseObject("MooseApp", ADMatchedValueBC);
+
+InputParameters
+ADMatchedValueBC::validParams()
+{
+  InputParameters params = ADNodalBC::validParams();
+  params.addRequiredCoupledVar("v", "The variable whose value we are to match.");
+  params.addClassDescription("Implements a nodal BC which equates two different Variables' values "
+                             "on a specified boundary.");
+  return params;
+}
+
+ADMatchedValueBC::ADMatchedValueBC(const InputParameters & parameters)
+  : ADNodalBC(parameters), _v(adCoupledValue("v"))
+{
+}
+
+ADReal
+ADMatchedValueBC::computeQpResidual()
+{
+  return _u - _v[_qp];
+}

test/tests/bcs/ad_matched_value_bc/test.i

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+[Mesh]
+  [square]
+    type = GeneratedMeshGenerator
+    nx = 2
+    ny = 2
+    dim = 2
+  []
+[]
+
+# Solves a pair of coupled diffusion equations where u=v on the boundary
+
+[Variables]
+  [u]
+    order = FIRST
+    family = LAGRANGE
+    initial_condition = 3
+  []
+
+  [v]
+    order = FIRST
+    family = LAGRANGE
+    initial_condition = 2
+  []
+[]
+
+[Kernels]
+  [diff_u]
+    type = ADDiffusion
+    variable = u
+  []
+
+  [diff_v]
+    type = ADDiffusion
+    variable = v
+  []
+[]
+
+[BCs]
+  [right_v]
+    type = ADDirichletBC
+    variable = v
+    boundary = 1
+    value = 3
+  []
+
+  [left_u]
+    type = ADMatchedValueBC
+    variable = u
+    boundary = 3
+    v = v
+  []
+[]
+
+[Executioner]
+  type = Steady
+  solve_type = 'NEWTON'
+
+  nl_rel_tol = 1e-10
+  l_tol = 1e-12
+[]
+
+[Outputs]
+  file_base = out
+  exodus = true
+[]

test/tests/bcs/ad_matched_value_bc/tests

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+[Tests]
+  requirement = "MOOSE shall support matching variable values on a boundary using automatic differentiation"
+  design = 'ADMatchedValueBC.md'
+  issues = "#18212"
+  [test]
+    type = 'Exodiff'
+    input = 'test.i'
+    exodiff = 'out.e'
+    detail = ''
+  []
+  [jacobian]
+    type = 'PetscJacobianTester'
+    input = 'test.i'
+    ratio_tol = 1e-8
+    difference_tol = 1e-7
+    detail = 'and shall be able to produce the exact Jacobian'
+  []
+[]