feat(NonlinearPowerIntergrator): increased robustness to theta ~ 0 and theta < 0

src/poly/utils/public/integrators.h

@@ -73,5 +73,30 @@ namespace polyMFEMUtils {
     Probe::LogManager& m_logManager = Probe::LogManager::getInstance();
     quill::Logger* m_logger = m_logManager.getLogger("log");
     double m_polytropicIndex;
+    double m_epsilon;
   };
+
+  inline double dfmod(const double epsilon, const double n) {
+    if (n == 0.0) {
+      return 0.0;
+    }
+    if (n == 1.0) {
+      return 1.0;
+    }
+    return n * std::pow(epsilon, n - 1.0);
+  }
+
+  inline double fmod(const double theta, const double n, const double epsilon) {
+    if (n == 0.0) {
+      return 1.0;
+    }
+    // For n != 0
+    const double y_prime_at_epsilon = dfmod(epsilon, n); // Uses the robust dfmod
+    const double y_at_epsilon = std::pow(epsilon, n);     // epsilon^n
+
+    // f_mod(theta) = y_at_epsilon + y_prime_at_epsilon * (theta - epsilon)
+    return y_at_epsilon + y_prime_at_epsilon * (theta - epsilon);
+  }
+
+
 } // namespace polyMFEMUtils