Velocity-Implicit Euler Fixed Step - Second PR of #12528

systems/analysis/BUILD.bazel

@@ -35,6 +35,7 @@ drake_cc_package_library(
         ":simulator",
         ":simulator_status",
         ":stepwise_dense_output",
+        ":velocity_implicit_euler_integrator",
     ],
 )
 
@@ -215,6 +216,18 @@ drake_cc_library(
     ],
 )
 
+drake_cc_library(
+    name = "velocity_implicit_euler_integrator",
+    srcs = ["velocity_implicit_euler_integrator.cc"],
+    hdrs = [
+        "velocity_implicit_euler_integrator.h",
+    ],
+    deps = [
+        ":implicit_integrator",
+        "//math:compute_numerical_gradient",
+    ],
+)
+
 drake_cc_library(
     name = "implicit_integrator",
     srcs = ["implicit_integrator.cc"],
@@ -435,7 +448,10 @@ drake_cc_googletest(
     deps = [
         ":implicit_euler_integrator",
         ":radau_integrator",
-        "//systems/analysis/test_utilities",
+        "//systems/analysis/test_utilities:cubic_scalar_system",
+        "//systems/analysis/test_utilities:implicit_integrator_test",
+        "//systems/analysis/test_utilities:linear_scalar_system",
+        "//systems/analysis/test_utilities:quadratic_scalar_system",
         "//systems/plants/spring_mass_system",
     ],
 )
@@ -508,6 +524,18 @@ drake_cc_googletest(
     ],
 )
 
+drake_cc_googletest(
+    name = "velocity_implicit_euler_integrator_test",
+    # Note: if memcheck takes too long with Valgrind, disable
+    # memcheck (per Drake issue #9621).
+    timeout = "moderate",
+    shard_count = 2,
+    deps = [
+        ":velocity_implicit_euler_integrator",
+        "//systems/analysis/test_utilities:implicit_integrator_test",
+    ],
+)
+
 drake_cc_googletest(
     name = "initial_value_problem_test",
     timeout = "moderate",

systems/analysis/implicit_integrator.h

@@ -394,6 +394,20 @@ class ImplicitIntegrator : public IntegratorBase<T> {
   /// @copydoc IntegratorBase::DoStep()
   virtual bool DoImplicitIntegratorStep(const T& h) = 0;
 
+  // Methods for derived classes to increment the factorization and Jacobian
+  // evaluation counts.
+  void increment_num_iter_factorizations() {
+    ++num_iter_factorizations_;
+  }
+
+  void increment_jacobian_computation_derivative_evaluations(int count) {
+    num_jacobian_function_evaluations_ += count;
+  }
+
+  void increment_jacobian_evaluations() {
+    ++num_jacobian_evaluations_;
+  }
+
  private:
   bool DoStep(const T& h) final {
     bool result = DoImplicitIntegratorStep(h);

systems/analysis/test/radau_integrator_test.cc

@@ -9,8 +9,6 @@
 #include "drake/systems/analysis/test_utilities/implicit_integrator_test.h"
 #include "drake/systems/analysis/test_utilities/linear_scalar_system.h"
 #include "drake/systems/analysis/test_utilities/quadratic_scalar_system.h"
-#include "drake/systems/analysis/test_utilities/robertson_system.h"
-#include "drake/systems/analysis/test_utilities/stationary_system.h"
 
 namespace drake {
 namespace systems {

systems/analysis/test/velocity_implicit_euler_integrator_test.cc

@@ -0,0 +1,18 @@
+#include "drake/systems/analysis/velocity_implicit_euler_integrator.h"
+
+#include <gtest/gtest.h>
+
+#include "drake/systems/analysis/test_utilities/implicit_integrator_test.h"
+
+namespace drake {
+namespace systems {
+namespace analysis_test {
+
+// Test Velocity-Implicit Euler integrator on common implicit tests.
+typedef ::testing::Types<VelocityImplicitEulerIntegrator<double>> MyTypes;
+INSTANTIATE_TYPED_TEST_SUITE_P(My, ImplicitIntegratorTest, MyTypes);
+
+}  // namespace analysis_test
+
+}  // namespace systems
+}  // namespace drake

systems/analysis/test_utilities/BUILD.bazel

@@ -94,7 +94,12 @@ drake_cc_library(
     testonly = 1,
     hdrs = ["implicit_integrator_test.h"],
     deps = [
+        ":discontinuous_spring_mass_damper_system",
+        ":linear_scalar_system",
         ":my_spring_mass_system",
+        ":robertson_system",
+        ":stationary_system",
+        ":stiff_double_mass_spring_system",
         "//common/test_utilities:expect_no_throw",
     ],
 )

systems/analysis/velocity_implicit_euler_integrator.cc

@@ -0,0 +1,5 @@
+#include "drake/systems/analysis/velocity_implicit_euler_integrator.h"
+
+DRAKE_DEFINE_CLASS_TEMPLATE_INSTANTIATIONS_ON_DEFAULT_NONSYMBOLIC_SCALARS(
+    class ::drake::systems::VelocityImplicitEulerIntegrator)
+